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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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 $ {T_1}$-space Y and a $ {T_3}$-space V, consider $ {T_3}$-spaces X such that X has a closed covering by spaces homeomorphic to V and any continuous mapping $ f:\,X \to Y$ 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