A subset of n-space retains it if any infinite subset has at least one accumulation point in the set, and it is equivalent to being closed and bounded under the Heine-Borel theorem.
A technique named for Wallman is used to impart this property to T1 spaces, and that method is the same as one named for Stone and Cech for normal spaces. The Arzelà–Ascoli theorem gives conditions for whether continuous functions from a metric space with this property preserve it and the product of spaces with this property retains this property under (*) Tychonoff's theorem. A subset of n-space retains it if any infinite subset has at least one accumulation point in the set, and it is equivalent to being closed and bounded under the Heine-Borel theorem. For 10 points, name this property of topological spaces, defined as each open cover having a finite subcover.
A technique named for Wallman is used to impart this property to T1 spaces, and that method is the same as one named for Stone and Cech for normal spaces.
{Compact}ness or any equivalent word forms