Door space: Difference between revisions

Revision as of 23:59, 18 February 2009

Citable Version ^[?]

This editable Main Article is under development and subject to a disclaimer.

[edit intro]

In topology, a door space is a topological space in which each subset is open or closed or both.

A discrete space is a door space since each subset is both open and closed.
The subset $\{0\}\cup \{1/n:n=1,2,\ldots \}$ of the real numbers with the usual topology is a door space. Any set containing the point 0 is closed: any set not containing the point 0 is open.

Revision as of 23:58, 18 February 2009 (view source) imported>Chris Day No edit summary ← Older edit		Revision as of 23:59, 18 February 2009 (view source) imported>Chris Day No edit summary Newer edit →
Line 1:		Line 1:
	{{subpages}}		{{subpages}}
	In [[topology]], a '''door space''' is a [[topological space]] in which each [[subset]] is [[open set\|open]] or [[closed set\|closed]] or both.		In [[topology]], a '''door space''' is a [[topological space]] in which each [[subset]] is [[open set\|open]] or [[closed set\|closed]] or both.