countable subset

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• Countable tightness — In mathematics, a topological space X is said to have countable tightness if it satisfies the condition::Given any subset A subset X, if x in overline{A}, there is a countable subset B subset A such that x in overline{B}.A prototypical example of …   Wikipedia

• Countable set — Countable redirects here. For the linguistic concept, see Count noun. Not to be confused with (recursively) enumerable sets. In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of… …   Wikipedia

• subset — UK [ˈsʌbˌset] / US noun [countable] Word forms subset : singular subset plural subsets a small group of people or things that is a part of a larger group Each patient is likely to show only a subset of the symptoms listed …   English dictionary

• countable — adjective a) Capable of being counted; having a quantity or a numerical attribute. b) Having a bijection with a subset of the natural numbers. Syn: denumerable Ant: uncountable …   Wiktionary

• Large countable ordinal — In the mathematical discipline of set theory, there are many ways of describing specific countable ordinals. The smallest ones can be usefully and non circularly expressed in terms of their Cantor normal forms. Beyond that, many ordinals of… …   Wikipedia

• Second-countable space — In topology, a second countable space, also called a completely separable space, is a topological space satisfying the second axiom of countability. A space is said to be second countable if its topology has a countable base. More explicitly,… …   Wikipedia

• First-countable space — In topology, a branch of mathematics, a first countable space is a topological space satisfying the first axiom of countability . Specifically, a space, X , is said to be first countable if each point has a countable neighbourhood basis (local… …   Wikipedia

• Axiom of countable choice — The axiom of countable choice or axiom of denumerable choice, denoted ACω, is an axiom of set theory, similar to the axiom of choice. It states that any countable collection of non empty sets must have a choice function. Spelled out, this means… …   Wikipedia

• Hereditarily countable set — In set theory, a set is called hereditarily countable if and only if it is a countable set of hereditarily countable sets. This inductive definition is in fact well founded and can be expressed in the language of first order set theory. A set is… …   Wikipedia

• Polish space — In mathematics, a Polish space is a separable completely metrizable topological space; that is, a space homeomorphic to a complete metric space that has a countable dense subset. Polish spaces are so named because they were first extensively… …   Wikipedia

• Complete Boolean algebra — This article is about a type of mathematical structure. For complete sets of Boolean operators, see Functional completeness. In mathematics, a complete Boolean algebra is a Boolean algebra in which every subset has a supremum (least upper bound) …   Wikipedia