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Gδ space
In mathematics, particularly topology, a Gδ space a space in which closed sets are ‘separated’ from their complements using only countably many open sets. A Gδ space may thus be regarded as a space satisfying a different kind of separation axiom. In fact normal Gδ spaces are referred to as perfectly normal spaces, and satisfy the strongest of separation axioms.
Gδ spaces are also called perfect spaces. The term ''perfect'' is also used, incompatibly, to refer to a space with no isolated points; see perfect space.
==Definition==
A subset of a topological space is said to be a Gδ set if it can be written as the countable intersection of open sets. Trivially, any open subset of a topological space is a Gδ set.
A topological space ''X'' is said to be a Gδ space if every closed subspace of ''X'' is a Gδ set (Steen and Seebach 1978, p. 162).
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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