Door space: Difference between revisions
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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. | ||
Latest revision as of 00:59, 19 February 2009
In topology, a door space is a topological space in which each subset is open or closed or both.
Examples
- A discrete space is a door space since each subset is both open and closed.
- The subset 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.
References
- J.L. Kelley (1955). General topology. van Nostrand, 76.