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N-topological space : ウィキペディア英語版 | N-topological space
In mathematics, an ''N''-topological space is a set equipped with ''N'' arbitrary topologies. If ''τ''1, ''τ''2, ..., ''τ''''N'' are ''N'' topologies defined on a nonempty set X, then the ''N''-topological space is denoted by (''X'',''τ''1,''τ''2,...,''τ''''N''). For ''N'' = 1, the structure is simply a topological space. For ''N'' = 2, the structure becomes a bitopological space introduced by J. C. Kelly. == Example == Let ''X'' = be any finite set. Suppose ''A''''r'' = . Then the collection ''τ''1 = will be a topology on ''X''. If ''τ''1, ''τ''2, ..., ''τ''''m'' be ''m'' such topologies (chain topologies) defined on ''X'', then the structure (''X'', ''τ''1, ''τ''2, ..., ''τ''''m'') is an ''m''-topological space.
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