extended topology

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• Topology — (Greek topos , place, and logos , study ) is the branch of mathematics that studies the properties of a space that are preserved under continuous deformations. Topology grew out of geometry, but unlike geometry, topology is not concerned with… …   Wikipedia

• Extended real number line — Positive infinity redirects here. For the band, see Positive Infinity. In mathematics, the affinely extended real number system is obtained from the real number system R by adding two elements: +∞ and −∞ (read as positive infinity and negative… …   Wikipedia

• topology — topologic /top euh loj ik/, topological, adj. topologically, adv. topologist, n. /teuh pol euh jee/, n., pl. topologies for 3. Math. 1. the study of those properties of geometric forms that remain invariant under c …   Universalium

• Topology (electronics) — The topology of an electronic circuit is the form taken by the network of interconnections of the circuit components. Different specific values or ratings of the components are regarded as being the same topology.Strictly speaking, replacing a… …   Wikipedia

• Long line (topology) — In topology, the long line (or Alexandroff line) is a topological space analogous to the real line, but much longer. Because it behaves locally just like the real line, but has different large scale properties, it serves as one of the basic… …   Wikipedia

• Network topology — Diagram of different network topologies. Network topology is the layout pattern of interconnections of the various elements (links, nodes, etc.) of a computer[1][2] …   Wikipedia

• Counterexamples in Topology —   Author(s) Lynn Arthur Steen J. Ar …   Wikipedia

• List of general topology topics — This is a list of general topology topics, by Wikipedia page. Contents 1 Basic concepts 2 Limits 3 Topological properties 3.1 Compactness and countability …   Wikipedia

• Digital topology — deals with properties and features of two dimensional (2D) or three dimensional (3D) digital images that correspond to topological properties (e.g., connectedness) or topological features (e.g., boundaries) of objects. Concepts and results of… …   Wikipedia

• Algebraic topology — is a branch of mathematics which uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism. In many situations this is too much to hope for… …   Wikipedia

• Alexandrov topology — In topology, an Alexandrov space (or Alexandrov discrete space) is a topological space in which the intersection of any family of open sets is open. It is an axiom of topology that the intersection of any finite family of open sets is open. In an …   Wikipedia