Definition:Weakly Locally Compact Space

Definition
Let $T = \left({S, \tau}\right)$ 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
 * Definition:Strongly Locally Compact
 * Definition:Sigma-Locally Compact
 * Locally Compact implies Weakly Locally Compact, whence the name weakly
 * Compact Space is Weakly Locally Compact
 * Sequence of Implications of Local Compactness Properties