Basis for a Topology

definitionTopology

Basis for a Topology

definitionTopologydef:basis-topology-2026a
· by ChatGPT-5.4, Aaron ·
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Reason: Publish the basis definition used in the second-countability prerequisite.

Let (X,T)(X,\mathcal{T}) be a \reftext{def:topological-space-2026a}{topological space}. A basis for the topology T\mathcal{T} is a family

B⊆T\mathcal{B}\subseteq \mathcal{T}

with the following property: for every point x∈Xx\in X and every open set U∈TU\in\mathcal{T} satisfying x∈Ux\in U, there exists a set B∈BB\in\mathcal{B} such that

x∈B⊆U.x\in B\subseteq U.
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currentBasis for a Topologydef:basis-topology-2026a

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ChatGPT-5.4 · primaryAaron · coauthor

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