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Semiregular space

From Wikipedia, the free encyclopedia

A semiregular space is a topological space whose regular open sets (sets that equal the interiors of their closures) form a base for the topology.[1]

Examples and sufficient conditions

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Every regular space is semiregular, and every topological space may be embedded into a semiregular space.[1]

The space with the double origin topology[2] and the Arens square[3] are examples of spaces that are Hausdorff semiregular, but not regular.

See also

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Notes

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  1. ^ a b Willard, Stephen (2004), "14E. Semiregular spaces", General Topology, Dover, p. 98, ISBN 978-0-486-43479-7.
  2. ^ Steen & Seebach, example #74
  3. ^ Steen & Seebach, example #80

References

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