Definition:Weakly Locally Compact Space

Definition
Let $T = \struct {S, \tau}$ be a topological space.

Then $T$ is weakly locally compact 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