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locally regular space
In mathematics, particularly topology, a topological space ''X'' is locally regular if intuitively it looks locally like a regular space. More precisely, a locally regular space satisfies the property that each point of the space belongs to an open subset of the space that is regular under the subspace topology.
==Formal definition==
A topological space ''X'' is said to be locally regular if and only if each point, ''x'', of ''X'' has a neighbourhood that is regular under the subspace topology. Equivalently, a space ''X'' is locally regular if and only if the collection of all open sets that are regular under the subspace topology forms a base for the topology on ''X''.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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