Definition:Local Basis/Neighborhood Basis of Open Sets
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Definition
Let $T = \struct {S, \tau}$ be a topological space.
Let $x$ be an element of $S$.
A local basis at $x$ is a set $\BB$ of open neighborhoods of $x$ such that every neighborhood of $x$ contains a set in $\BB$.
That is, a local basis at $x$ is a neighborhood basis of $x$ consisting of open sets.
Also see
Sources
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $1$: General Introduction: Countability Properties