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In topology and related fields of mathematics, a sequential space is a topological space that satisfies a very weak axiom of countability. Sequential spaces are the most general class of spaces for which sequences suffice to determine the topology. Every sequential space has countable tightness. == Definitions == Let ''X'' be a topological space. *A subset ''U'' of ''X'' is sequentially open if each sequence (''x''''n'') in ''X'' converging to a point of ''U'' is eventually in ''U'' (i.e. there exists ''N'' such that ''x''''n'' is in ''U'' for all ''n'' ≥ ''N''.) *A subset ''F'' of ''X'' is sequentially closed if, whenever (''x''''n'') is a sequence in ''F'' converging to ''x'', then ''x'' must also be in ''F''. The complement of a sequentially open set is a sequentially closed set, and vice versa. Every open subset of ''X'' is sequentially open and every closed set is sequentially closed. The converses are not generally true. A sequential space is a space ''X'' satisfying one of the following equivalent conditions: #Every sequentially open subset of ''X'' is open. #Every sequentially closed subset of ''X'' is closed. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Sequential space」の詳細全文を読む スポンサード リンク
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