Category:Definitions/Local Bases
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This category contains definitions related to Local Bases.
Related results can be found in Category:Local Bases.
Let $T = \struct {S, \tau}$ be a topological space.
Let $x$ be an element of $S$.
Local Basis for Open Sets
A local basis at $x$ is a set $\BB$ of open neighborhoods of $x$ such that:
- $\forall U \in \tau: x \in U \implies \exists H \in \BB: H \subseteq U$
That is, such that every open neighborhood of $x$ also contains some set in $\BB$.
Neighborhood Basis of Open Sets
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.
Pages in category "Definitions/Local Bases"
The following 3 pages are in this category, out of 3 total.