Topological spaces with prescribed nonconstant continuous mappings

Author:
Věra Trnková

Journal:
Trans. Amer. Math. Soc. **261** (1980), 463-482

MSC:
Primary 54C05; Secondary 20M20, 54H10

DOI:
https://doi.org/10.1090/S0002-9947-1980-0580898-9

MathSciNet review:
580898

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Abstract: Given a -space *Y* and a -space *V*, consider -spaces *X* such that *X* has a closed covering by spaces homeomorphic to *V* and any continuous mapping is constant. All such spaces and all their continuous mappings are shown to form a very comprehensive category, containing, e.g., a proper class of spaces without nonconstant, nonidentical mappings or containing a space *X*, for every monoid *M*, such that all the nonconstant continuous mappings of *X* into itself are closed under composition and form a monoid isomorphic to *M*. The category of paracompact connected spaces, having a closed covering by a given totally disconnected paracompact space, has, e.g., analogous properties. Categories of metrizable spaces are also investigated.

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DOI:
https://doi.org/10.1090/S0002-9947-1980-0580898-9

Article copyright:
© Copyright 1980
American Mathematical Society