Door space: Difference between revisions

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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.

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	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.