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.^[1]

Examples and sufficient conditions

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

The space ${\displaystyle X=\mathbb {R} ^{2}\cup \{0^{*}\}}$ with the double origin topology^[2] and the Arens square^[3] are examples of spaces that are Hausdorff semiregular, but not regular.

See also

• Separation axiom – Axioms in topology defining notions of "separation"