Hemicompact space

Symbol-free definition
A topological space is termed hemicompact if it is the union of an ascending sequence of compact subsets, each contained in the interior of the next, such that every compact subset is contained in one of these.

Definition with symbols
A topological space $$X$$ is termed hemicompact if there is a sequence $$K_n$$ of compact subsets such that $$K_n \subset int K_{n+1}$$, and such that any compact subset is contained in $$K_n$$ for some $$n$$.

Stronger properties

 * Compact space

Weaker properties

 * Sigma-compact space