Definition:Compact Space/Topology/Definition 3

Definition

A topological space $T = \struct {S, \tau}$ is compact if and only if $\tau$ has a sub-basis $\BB$ such that:

from every cover of $S$ by elements of $\BB$, a finite subcover of $S$ can be selected.

Also see

• Equivalence of Definitions of Compact Topological Space

• Results about 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: Global Compactness Properties