exceptional subset

1) телефон. абонентский аппарат

2) подгруппа

3) подкласс

4) подмножество

5) полукомплект

6) сокращённый вариант

•

- absolutely convex subset

- absorbent subset

- algebraic subset

- almost clopen subset

- analytic subset

- arcwise connected subset

- balanced subset

- benign subset

- bicompact subset

- bifurcation subset

- biperfect subset

- bistrong subset

- bounded above subset

- bounded subset

- calculable subset

- circled subset

- clopen subset

- closed subset

- cofinal subset

- coinitial subset

- coisotropic subset

- compactly circled subset

- complementary subset

- complete subset

- completely ordered subset

- computable subset

- conditionally compact subset

- connected subset

- constructive subset

- convex subset

- countable subset

- countably compact subset

- countercompact subset

- critical subset

- cubic subset

- dense subset

- dense-in-itself subset

- dependent subset

- diagonal subset

- directed subset

- discriminant subset

- disjunctive subset

- distinguished subset

- doubly transitive subset

- elementary subset

- empty subset

- enumerable subset

- evenly covered subset

- exceptional subset

- exclusive subset

- extremal subset

- faithful subset

- finite subset

- finitely connected subset

- flat subset

- free subset

- fully invariant subset

- fundamental subset

- fuzzy subset

- generic subset

- imprimitive subset

- improper subset

- independent subset

- indexed subset

- indiscernible subset

- infinite subset

- inseparable subset

- invariant subset

- inversely invariant subset

- invertible subset

- irredundant subset

- isolated subset

- left unitary subset

- linear subset

- linearly dependent subset

- maximal subset

- meager subset

- measurable subset

- metrizable subset

- multiperiodic subset

- multiplicative subset

- multiplicatively closed subset

- negligible subset

- nonempty subset

- non-empty subset

- nonnull subset

- nonvacuous subset

- normal subset

- nowhere dense subset

- numeral subset

- open-closed subset

- order-bounded subset

- order-complete subset

- order-dense subset

- ordered subset

- partial subset

- polygonally connected subset

- prenuclear subset

- prevalent subset

- primary subset

- pseudocompact subset

- purely inseparable subset

- quasiclosed subset

- quasicomplete subset

- quasistable subset

- radial subset

- rare subset

- rationally independent subset

- receiver subset

- rectifiable subset

- recursive subset

- recursively enumerable subset

- reflexive subset

- regular subset

- regularly situated subsets

- retraceable subset

- right neat subset

- saturated subset

- scattered subset

- semianalytic subset

- semiclosed subset

- semilinear subset

- separated subset

- separating subset

- sequentially compact subset

- simplicial subset

- simply bounded subset

- solid subset

- solvable subset

- starlike subset

- stationary subset

- strict subset

- strictly separated subset

- subanalytic subset

- subset relation

- symmetric subset

- syndetic subset

- tame subset

- thick subset

- total subset

- totally bounded subset

- transmitter subset

- trivial subset

- true subset

- ubiquitous subset

- uncountable subset

- uniformly embedded subset

χάρις, ιτος, ἡ (Hom.+) acc. quite predom. χάριν, but χάριτα Ac 24:27; 25:9 v.l.; Jd 4 and pl. χάριτας Ac 24:27 v.l.; 1 Cl 23:1 (Eur., Hel. 1378; Hdt. 6, 41; X., Hell. 3, 5, 16; ins, pap; Zech 4:7; 6:14; EpArist 272, pl. 230.—B-D-F §47, 3; W-S. §9, 7; Mayser 271f; Thackeray 150; Helbing 40f; Mlt-H. 132.—It seems that χάρις is not always clearly differentiated in mng. fr. χαρά; Apollodorus [II B.C.]: 244 Fgm. 90 Jac. says in the second book περὶ θεῶν: κληθῆναι δὲ αὐτὰς ἀπὸ μὲν τ. χαρᾶς Χάριτας• καὶ γὰρ πολλάκις … οἱ ποιηταὶ τ. χάριν χαρὰν καλοῦσιν ‘the [deities] Charites are so called from χαρά [joy], for poets freq. equate χάρις with χαρά’. Cp. the wordplay AcPl Ha 8, 7 χαρᾶς καὶ χάριτος the house was filled with gaiety and gratitude.).

① a winning quality or attractiveness that invites a favorable reaction, graciousness, attractiveness, charm, winsomeness (Hom.+; Jos., Ant. 2, 231) of human form and appearance παῖς λίαν εὐειδής ἐν χάριτι an exceptionally fine-looking and winsome youth AcPl Ha 3, 13. Of speech (Demosth. 51, 9; Ps.-Demetr. [I A.D.], Eloc. §127; 133; 135 al.; Eccl 10:12; Sir 21:16; Jos., Ant. 18, 208) οἱ λόγοι τῆς χάριτος (gen. of quality) the gracious words Lk 4:22. ὁ λόγος ὑμῶν πάντοτε ἐν χάριτι let your conversation always be winsome Col 4:6 (cp. Plut., Mor. 514f; s. also HAlmqvist, Plut. u. das NT ’46, 121f; Epict. 3, 22, 90). τὸ πρόσωπον αὐτοῦ χάριτος ἐπληροῦτο MPol 12:1 can also be placed here in case χάρις means nothing more than graciousness (s. 4 below); prob. also GJs 7:3 (s. 3b).

② a beneficent disposition toward someone, favor, grace, gracious care/help, goodwill (almost a t.t. in the reciprocity-oriented world dominated by Hellenic influence [cp. e.g. OGI 669, 29] as well as by the Semitic sense of social obligation expressed in the term חֶסֶד [NGlueck, Das Wort ḥesed in alttestamentlichen Sprachgebrauche etc. 1927]. Of a different order and spirit is the subset of reciprocity known as Roman patronage, in which superiority of the donor over the client is clearly maintained)

ⓐ act., that which one grants to another, the action of one who volunteers to do someth. not otherwise obligatory χάρις θεοῦ ἦν ἐπʼ αὐτό Lk 2:40. ἡ χάρις τοῦ θεοῦ (cp. τῇ τοῦ θεοῦ Κλαυδίου χάριτι OGI 669, 29) Ac 11:2 D; 14:26. τοῦ κυρίου 15:40.—Esp. of the beneficent intention of God (cp. χ. in reference to God: Apollon. Rhod. 3, 1005 σοὶ θεόθεν χάρις ἔσσεται; Dio Chrys. 80 [30], 40 χ. τῶν θεῶν; Ael. Aristid. 13 p. 320 D.; 53 p. 620; Sextus 436b; likew. in LXX, Philo, Joseph.; SibOr 4, 46=189; 5, 330; Ezk. Trag. 162 [Eus., PE 9, 29, 12].—χ. to denote beneficent dispensations of the emperor: OGI 669, 44 [I A.D.]; BGU 19 I, 21 [II A.D.] χάρ. τοῦ θεοῦ Αὐτοκράτορος; 1085 II, 4) and of Christ, who give (undeserved) gifts to people; God: δικαιούμενοι δωρεὰν τῇ αὐτοῦ χάριτι Ro 3:24. Cp. 5:15a, 20f; 6:1; 11:5 (ἐκλογή 1), 6abc; Gal 1:15 (διά A 3e); Eph 1:6f (KKuhn, NTS 7, ’61, 337 [reff. to Qumran lit.]); 2:5, 7, 8; cp. Pol 1:3; 2 Th 1:12; 2:16; 2 Ti 1:9; Tit 2:11 (ἡ χάρ. τοῦ θεοῦ σωτήριος; s. Dibelius, Hdb. exc. after Tit 2:14); 3:7; Hb 2:9 (χωρίς 2aα); 4:16a (DdeSilva, JBL 115, ’96, 100–103); 1 Cl 50:3; ISm 9:2; IPol 7:3. ἐν χάρ[ιτι θεοῦ] AcPl Ha 7, 23 (restoration uncertain). κατὰ χάριν as a favor, out of goodwill (cp. Pla., Leg. 740c; schol. on Soph., Oed. Col. 1751 p. 468 Papag.) Ro 4:4 (opp. κατὰ ὀφείλημα), 16.—The beneficence or favor of Christ: διὰ τῆς χάριτος τοῦ κυρίου Ἰησοῦ πιστεύομεν σωθῆναι Ac 15:11. Cp. Ro 5:15b; 2 Cor 8:9; 1 Ti 1:14; IPhld 8:1. On Ac 2:47 in this sense s. TAnderson, NTS 34, ’88, 604–10.

ⓑ pass., that which one experiences fr. another (Arrian, Anab. Alex. 3, 26, 4) χάριν ἔχειν have favor 3J 4 v.l. πρός τινα with someone=win his respect Ac 2:47 (cp. 2a end; cp. Pind., O. 7, 89f χάριν καὶ ποτʼ ἀστῶν καὶ ποτὶ ξείνων grant him respect in the presence of his townfolk as well as strangers); παρά τινι (Appian, Bell. Civ. 2, 89 §376) Hm 10, 3, 1, cp. 5, 1, 5. εὑρεῖν χάριν παρά τινι (Philo, Leg. All. 3, 77, end) Lk 1:30; Hs 5, 2, 10; ἐνώπιόν τινος Ac 7:46; GJs 11:2 (JosAs 15:14). ἐν τοῖς μέλλουσι μετανοεῖν among those who are about to repent Hm 12, 3, 3. Ἰησοῦς προέκοπτεν χάριτι παρὰ θεῷ καὶ ἀνθρώποις Lk 2:52 (an indication of exceptional ἀρετή, cp. Pind. above). Cp. Ac 4:33; 7:10 (ἐναντίον Φαραώ); Hb 4:16b.—ποία ὑμῖν χάρις ἐστίν; what credit is that to you? Lk 6:32–34; s. D 1:3; 2 Cl 13:4. Cp. 1 Cor 9:16 v.l. In these passages the mng. comes close to reward (s. Wetter [5 below] 209ff w. reff.).—Also by metonymy that which brings someone (God’s) favor or wins a favorable response fr. God 1 Pt 2:19, 20.

ⓒ In Christian epistolary lit. fr. the time of Paul χάρις is found w. the sense (divine) favor in fixed formulas at the beginning and end of letters (Zahn on Gal 1:3; vDobschütz on 1 Th 1:1; ELohmeyer, ZNW 26, 1927, 158ff; APujol, De Salutat. Apost. ‘Gratia vobis et pax’: Verb. Dom. 12, ’32, 38–40; 76–82; WFoerster, TW II ’34, 409ff; Goodsp., Probs. 141f. S. also the lit. s.v. χαίρω 2b). At the beginning of a letter χάρις ὑμῖν καὶ εἰρήνη (sc. εἴη; New Docs 8, 127f) Ro 1:7; 1 Cor 1:3; 2 Cor 1:2; Gal 1:3; Eph 1:2; Phil 1:2; Col 1:2; 1 Th 1:1; 2 Th 1:2; Phlm 3; Rv 1:4; without ὑμῖν Tit 1:4. χάρις ὑμῖν καὶ εἰρήνη πληθυνθείη 1 Pt 1:2; 2 Pt 1:2; 1 Cl ins. χάρις, ἔλεος, εἰρήνη 1 Ti 1:2; 2 Ti 1:2; 2J 3 (on the triplet cp. En 5:7 φῶς καὶ χάρις καὶ εἰρήνη).—At the end ἡ χάρις (τοῦ κυρίου ἡμῶν Ἰησοῦ Χριστοῦ etc.) μεθʼ ὑμῶν (or μετὰ πάντων ὑμῶν etc.) Ro 16:20, 23 (24) v.l.; 1 Cor 16:23; 2 Cor 13:13; Gal 6:18; Eph 6:24; Phil 4:23; Col 4:18; 1 Th 5:28; 2 Th 3:18; 1 Ti 6:21; 2 Ti 4:22; Tit 3:15; Phlm 25; Hb 13:25; Rv 22:21; 1 Cl 65:2. ἔσται ἡ χάρις μετὰ πάντων τῶν φοβουμένων τὸν Κύριον GJs 25:2. ὁ κύριος τῆς δόξης καὶ πάσης χάριτος μετὰ τοῦ πνεύματος ὑμῶν B 21:9. χάρις ὑμῖν, ἔλεος, εἰρήνη, ὑπομονὴ διὰ παντός ISm 12:2. ἔρρωσθε ἐν χάριτι θεοῦ 13:2.

③ practical application of goodwill, (a sign of) favor, gracious deed/gift, benefaction

ⓐ on the part of humans (X., Symp. 8, 36, Ages. 4, 3; Appian, Bell. Civ. 1, 49 §213; Dionys. Hal. 2, 15, 4) χάριν (-ιτα) καταθέσθαι τινί (κατατίθημι 2) Ac 24:27; 25:9. αἰτεῖσθαι χάριν 25:3 (in these passages from Ac χ. suggests [political] favor, someth. one does for another within a reciprocity system. Cp. Appian, Bell. Civ. 1, 108 §506 ἐς χάριν Σύλλα=as a favor to Sulla; ApcSed 8:1 οὐκ ἐποίησάς μοι χάριν=you did me no favor). ἵνα δευτέραν χάριν σχῆτε that you might have a second proof of my goodwill 2 Cor 1:15 (unless χάρις here means delight [so in poetry, Pind. et al., but also Pla., Isocr.; L-S-J-M s.v. χάρις IV; cp. also the quot. fr. Apollodorus at the beg. of the present entry, and the fact that χαρά is v.l. in 2 Cor 1:15]; in that case δευτέρα means double; but s. comm.). Of the collection for Jerusalem (cp. Appian, Bell. Civ. 3, 42 §173 χάριτας λαμβάνειν=receive gifts) 1 Cor 16:3; 2 Cor 8:4, 6f, 19 (DdeSilva, JBL 115, ’96, 101). Cp. B 21:7.—Eph 4:29 may suggest a demonstration of human favor (cp. Plut., Mor. 514e χάριν παρασκευάζοντες ἀλλήλοις), but a ref. to the means by which divine grace is mediated is not to be ruled out (s. b below).

ⓑ on the part of God and Christ; the context will show whether the emphasis is upon the possession of divine favor as a source of blessings for the believer, or upon a store of favor that is dispensed, or a favored status (i.e. standing in God’s favor) that is brought about, or a gracious deed wrought by God in Christ, or a gracious work that grows fr. more to more (so in contrast to the old covenant Mel., P. 3, 16 al.). God is called ὁ θεὸς πάσης χάριτος 1 Pt 5:10, i.e. God, who is noted for any conceivable benefit or favor; cp. B 21:9.—χάριν διδόναι τινί show favor to someone (Anacr. 110 Diehl; Appian, Ital. 5 §10): τὸν δόντα αὐτῷ τὴν χάριν GJs 14:2. ταπεινοῖς δίδωσι χάριν (Pr 3:34) Js 4:6b; 1 Pt 5:5; 1 Cl 30:2; without a dat. Js 4:6a (Menand., Epitr. 231 S. [55 Kö.]). Perh. καὶ ἔβαλλε κύριος … χάριν ἐπʼ αὐτήν GJs 7:3 (but s. 1 above). The Logos is πλήρης χάριτος J 1:14. Those who belong to him receive of the fullness of his grace, χάριν ἀντὶ χάριτος vs. 16 (ἀντί 2). Cp. vs. 17. τὴν χάριν ταύτην ἐν ᾗ ἑστήκαμεν this favor (of God) we now enjoy Ro 5:2 (Goodsp.).—5:17; 1 Cor 1:4; 2 Cor 4:15 (divine beneficence in conversion); cp. Ac 11:23; 6:1; Gal 1:6 (by Christ’s gracious deed); 2:21; 5:4; Col 1:6; 2 Ti 2:1; Hb 12:15; 13:9; 1 Pt 1:10, 13; 3:7 (συνκληρονόμοι χάριτος ζωῆς fellow-heirs of the gift that spells life; s. ζωή 2bα); 5:12; 2 Pt 3:18; Jd 4; IPhld 11:1; ISm 6:2. Christians stand ὑπὸ χάριν under God’s gracious will as expressed in their release from legal constraint Ro 6:14f, or they come ὑπὸ τὸν ζυγὸν τῆς χάριτος αὐτοῦ 1 Cl 16:17 (ζυγός 1). The proclamation of salvation is the message of divine beneficence τὸ εὐαγγέλιον τῆς χάριτος τοῦ θεοῦ Ac 20:24 or ὁ λόγος τῆς χάριτος αὐτοῦ (=τοῦ κυρίου) 14:3; 20:32. Even the gospel message can be called ἡ χάρις τοῦ θεοῦ 13:43; cp. 18:27; MPol 2:3. τὸ πνεῦμα τῆς χάριτος the Spirit from or through whom (God’s) favor is shown Hb 10:29 (AArgyle, Grace and the Covenant: ET 60, ’48/49, 26f).—Pl. benefits, favors (Diod S 3, 2, 4; 3, 73, 6; Sb 8139, 4 [ins of I B.C.] of Isis; Jos., C. Ap. 2, 190) 1 Cl 23:1.—Nelson Glueck, Das Wort ḥesed etc. 1927, but s. FAndersen, ‘Yahweh, the Kind and Sensitive God’: God Who is Rich in Mercy, ed. PO’Brien/DPeterson ’86.

④ exceptional effect produced by generosity, favor. Of effects produced by divine beneficence which go beyond those associated with a specific Christian’s status (ins μεγάλαι χάριτες τοῦ θεου: FCumont, Syria 7, 1926, 347ff), in the congregations of Macedonia 2 Cor 8:1 and Corinth 9:14; cp. vs. 8; in Rome AcPl Ha 7, 8. The Christian confessor is in full possession of divine grace ISm 11:1. Paul knows that through the χάρις of God he has been called to be an apostle, and that he has been fitted out w. the powers and capabilities requisite for this office fr. the same source: Ro 1:5; 12:3; 15:15; 1 Cor 3:10; 15:10ab (for the subject matter cp. Polyb. 12, 12b, 3 αὐτὸν [Alex. the Great] ὑπὸ τοῦ δαιμονίου τετευχέναι τούτων ὧν ἔτυχεν=whatever he has received he has received from what is divine. [For this reason he does not deserve any divine honors.]); 2 Cor 12:9; Gal 2:9; Eph 3:2, 7f; Phil 1:7.—The χάρις of God manifests itself in various χαρίσματα: Ro 12:6; Eph 4:7; 1 Pt 4:10. This brings into view a number of passages in which χάρις is evidently to be understood in a very concrete sense. It is hardly to be differentiated fr. δύναμις (θεοῦ) or fr. γνῶσις or δόξα (q.v. 1b. On this subj. s. Wetter [5 below] p. 94ff; esp. 130ff; pap in the GLumbroso Festschr. 1925, 212ff: χάρις, δύναμις, πνεῦμα w. essentially the same mng.; PGM 4, 2438; 3165; Herm. Wr. 1, 32; Just., D. 87, 5 ἀπὸ χάριτος τῆς δυνάμεως τοῦ πνεύματος). οὐκ ἐν σοφίᾳ σαρκικῇ ἀλλʼ ἐν χάριτι θεοῦ 2 Cor 1:12. οὐκ ἐγὼ δὲ ἀλλὰ ἡ χάρις τοῦ θεοῦ σὺν ἐμοί 1 Cor 15:10c. αὐξάνετε ἐν χάριτι καὶ γνώσει τοῦ κυρίου 2 Pt 3:18; cp. 1 Cl 55:3; B 1:2 (τῆς δωρεᾶς πνευματικῆς χάρις). Stephen is said to be πλήρης χάριτος καὶ δυνάμεως Ac 6:8. Divine power fills the Christian confessor or martyr w. a radiant glow MPol 12:1 (but s. 1 above). As the typical quality of the age to come, contrasted w. the κόσμος D 10:6.

⑤ response to generosity or beneficence, thanks, gratitude (a fundamental component in the Gr-Rom. reciprocity system; exx. fr. later times: Diod S 11, 71, 4 [χάριτες=proofs of gratitude]; Appian, Syr. 3, 12; 13. Cp. Wetter [below] p. 206f) χάριν ἔχειν τινί be grateful to someone (Eur., Hec. 767; X., An. 2, 5, 14; Pla., Phlb. 54d; Ath. 2, 1; PLips 104, 14 [I B.C.] χάριν σοι ἔχω) foll. by ὅτι (Epict. 3, 5, 10; Jos., C. Ap. 1, 270; 2, 49) Lk 17:9 (ERiggenbach, NKZ 34, 1923, 439–43); mostly of gratitude to God or Christ; χάρις in our lit. as a whole, in the sense gratitude, refers to appropriate respone to the Deity for benefits conferred (Hom., Pind., Thu. et al.; ins, pap, LXX; Jos., Ant. 7, 208) χάριν ἔχω τῷ θεῷ (POxy 113, 13 [II A.D.] χάριν ἔχω θεοῖς πᾶσιν.—Epict. 4, 7, 9) 2 Ti 1:3; foll. by ὅτι because 1 Ti 1:12 (Herm. Wr. 6, 4 κἀγὼ χάριν ἔχω τῷ θεῷ …, ὅτι; Jos., Ant. 4, 316); χάριν ἔχειν ἐπί τινι be grateful for someth. Phlm 7 v.l. (to humans). ἔχωμεν χάριν let us be thankful (to God) Hb 12:28 (the reason for it is given by the preceding ptc. παραλαμβάνοντες). Elliptically (B-D-F §128, 6; cp. Rob. 1201f) χάρις (ἔστω) τῷ θεῷ (X., Oec. 8, 16 πολλὴ χάρις τοῖς θεοῖς; Epict. 4, 4, 7 χάρις τῷ θεῳ; BGU 843, 6 [I/II A.D.] χάρις τοῖς θεοῖς al. in pap since III B.C..—Philo, Rer. Div. Her. 309) Ro 7:25; MPol 3:1. Foll. by ὅτι (X., An. 3, 3, 14 τοῖς θεοῖς χάρις ὅτι; PFay 124, 16 τοῖς θεοῖς ἐστιν χάρις ὅτι; Epict. 4, 5, 9) Ro 6:17. Foll. by ἐπί τινι for someth. (UPZ 108, 30 [99 B.C.]) 2 Cor 9:15. The reason for the thanks is given in the ptc. agreeing w. τῷ θεῷ 2:14; 8:16; 1 Cor 15:57 (cp. Jos., Ant. 6, 145; Philo, Somn. 2, 213). Thankfulness (Appian, Bell. Civ. 3, 15 §51 πρός τινα=toward someone) χάριτι in thankfulness 10:30. So prob. also ἐν τῇ χάριτι in a thankful spirit Col 3:16 (Dibelius, Hdb. ad loc.). πλησθῆναι χαρᾶς καὶ χάριτος AcPl Ha 8, 7. S. εὐχαριστέω, end. Also PSchubert, Form and Function of the Pauline Thanksgivings ’39.—OLoew, Χάρις, diss., Marburg 1908; GWetter, Charis 1913; AvHarnack, Sanftmut, Huld u. Demut in der alten Kirche: JKaftan Festschr. 1920, 113ff; NBonwetsch, Zur Geschichte des Begriffs Gnade in der alten Kirche: Harnack Festgabe 1921, 93–101; EBurton, Gal ICC 1921, 423f; WWhitley, The Doctrine of Grace ’32; JMoffatt, Grace in the NT ’31; RWinkler, D. Gnade im NT: ZST 10, ’33, 642–80; RHomann, D. Gnade in d. Syn. Ev.: ibid. 328–48; JWobbe, D. Charisgedanke b. Pls ’32; RBultmann, Theologie des NT ’48, 283–310 (Paul); HBoers, Ἀγάπη and Χάρις in Paul’s Thought: CBQ 59, ’97, 693–713; on 2 Cor 8: FDanker, Augsburg Comm. 2 Cor, 116–34; PRousselot, La Grâce d’après St. Jean et d’après St. Paul: SR 18, 1928, 87–108, Christent. u. Wissensch. 8, ’32, 402–30; JMontgomery, Hebrew Hesed and Gk. Charis: HTR 32, ’39, 97–102; Dodd 61f; TTorrance, The Doctrine of Grace in the Apost. Fathers, ’48; JRenié, Studia Anselmiana 27f, ’51, 340–50; CRSmith, The Bible Doctrine of Grace, ’56; EFlack, The Concept of Grace in Bibl. Thought: Bibl. Studies in Memory of HAlleman, ed. Myers, ’60, 137–54; DDoughty, NTS 19, ’73, 163–80.—B. 1166. DELG. M-M. EDNT. TW. Spicq. Sv.