countability axiom

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• axiom of countability — Math. the property satisfied by a topological space in which the neighborhood system of each point has a base consisting of a countable number of neighborhoods (first axiom of countability) or the property satisfied by a topological space that… …   Universalium

• axiom of countability — Math. the property satisfied by a topological space in which the neighborhood system of each point has a base consisting of a countable number of neighborhoods (first axiom of countability) or the property satisfied by a topological space that… …   Useful english dictionary

• 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

• first axiom of countability — Math. See under axiom of countability. * * * …   Universalium

• second axiom of countability — Math. See under axiom of countability. * * * …   Universalium

• first axiom of countability — Math. See under axiom of countability …   Useful english dictionary

• second axiom of countability — Math. See under axiom of countability …   Useful english dictionary

• List of mathematics articles (A) — NOTOC A A Beautiful Mind A Beautiful Mind (book) A Beautiful Mind (film) A Brief History of Time (film) A Course of Pure Mathematics A curious identity involving binomial coefficients A derivation of the discrete Fourier transform A equivalence A …   Wikipedia

• General topology — In mathematics, general topology or point set topology is the branch of topology which studies properties of topological spaces and structures defined on them. It is distinct from other branches of topology in that the topological spaces may be… …   Wikipedia

• Net (mathematics) — This article is about nets in topological spaces and not about ε nets in other fields. In mathematics, more specifically in general topology and related branches, a net or Moore–Smith sequence is a generalization of the notion of a sequence. In… …   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