The property O n for finite seminormal functors
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We give a finite combinatorial test for finite seminormal functors to possess the property On and use it in establishing that in some cases this property leads to some well-known functors. For example, if some functor F possesses the property O2 then F2 coincides with either exp2 or the squaring functor. Hence we conclude that if F(Dω1) and Dω1 are homeomorphic then F2 is either exp2 or (·)2.
Keywordscompact space open mapping seminormal functor finite functor exponential functor infinite-to-one mapping
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- 5.Fedorchuk V. V. and Filippov V. V., General Topology. Basic Constructions [in Russian], Moscow Univ., Moscow (1988).Google Scholar