point-countable base

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• Base (topology) — In mathematics, a base (or basis) B for a topological space X with topology T is a collection of open sets in T such that every open set in T can be written as a union of elements of B. We say that the base generates the topology T. Bases are… …   Wikipedia

• base — 1 /beIs/ verb (T) to establish or use somewhere as the main place for your business or work: a Denver based law firm base sth on/upon sth phrasal verb (transitive often passive) to use particular information or facts as a point from which to… …   Longman dictionary of contemporary English

• 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

• 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

• Glossary of topology — This is a glossary of some terms used in the branch of mathematics known as topology. Although there is no absolute distinction between different areas of topology, the focus here is on general topology. The following definitions are also… …   Wikipedia

• Topological property — In topology and related areas of mathematics a topological property or topological invariant is a property of a topological space which is invariant under homeomorphisms. That is, a property of spaces is a topological property if whenever a space …   Wikipedia

• Axiom of countability — In mathematics, an axiom of countability is a property of certain mathematical objects (usually in a category) that requires the existence of a countable set with certain properties, while without it such sets might not exist. Important… …   Wikipedia

• Domain theory — is a branch of mathematics that studies special kinds of partially ordered sets (posets) commonly called domains. Consequently, domain theory can be considered as a branch of order theory. The field has major applications in computer science,… …   Wikipedia

• G-delta space — In mathematics, particularly topology, a G delta; space a space in which closed sets are ‘separated’ from their complements using only countably many open sets. A G delta; space may thus be regarded as a space satisfying a different kind of… …   Wikipedia

• Inductive dimension — In the mathematical field of topology, the inductive dimension of a topological space X is either of two values, the small inductive dimension ind(X) or the large inductive dimension Ind(X). These are based on the observation that, in n… …   Wikipedia