Definition:Weakly Locally Compact Space
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Definition
Let $T = \struct {S, \tau}$ be a topological space.
Then $T$ is weakly locally compact if and only if every point of $S$ has a compact neighborhood.
Also known as
Some sources refer to this as locally compact, but modern developments have introduced a slightly stronger concept for which that term is usually used.
Also see
- Definition:Locally Compact Space
- Definition:Strongly Locally Compact Space
- Definition:$\sigma$-Locally Compact Space
- Definition:Weakly $\sigma$-Locally Compact Space
- Locally Compact Space is Weakly Locally Compact, whence the name weakly
- Sequence of Implications of Local Compactness Properties
- Results about weakly locally compact spaces can be found here.
Sources
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $3$: Compactness: Localized Compactness Properties
- but note that they use the term locally compact.