Semiregular space
A semiregular space is a topological space whose regular open sets form a base.
Every regular space is semiregular, and every topological space may be embedded into a semiregular space.
Semiregular spaces should not be confused with locally regular spaces, spaces in which there is a base of open sets that induce regular subspaces. For example, the bug-eyed line is locally regular but not semiregular.
