Semiregular space

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.

Examples and sufficient conditions

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

The space $X={ℝ}^2\cup \{0^{*}\}$ with the double origin topology and the Arens square are examples of spaces that are Hausdorff semiregular, but not regular.

See also

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References

• Lynn Arthur Steen and J. Arthur Seebach, Jr., Counterexamples in Topology. Springer-Verlag, New York, 1978. Reprinted by Dover Publications, New York, 1995. Template:ISBN (Dover edition).
• Template:Willard General Topology