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Stone functor : ウィキペディア英語版
Stone functor

In mathematics, the Stone functor is a functor ''S'': Topop → Bool, where Top is the category of topological spaces and Bool is the category of Boolean algebras and Boolean homomorphisms. It assigns to each topological space ''X'' the Boolean algebra ''S''(''X'') of its clopen subsets, and to each morphism ''f''op: ''X'' → ''Y'' in Topop (i.e., a continuous map ''f'': ''Y'' → ''X'') the homomorphism ''S''(''f''): ''S''(''X'') → ''S''(''Y'') given by ''S''(''f'')(''Z'') = ''f''−1().
==See also==

*Stone's representation theorem for Boolean algebras
*Pointless topology

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「Stone functor」の詳細全文を読む



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