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Spaces on which every Continuous Map into a given Space is Constant

Published online by Cambridge University Press:  20 November 2018

S. Iliadis  and
V. Tzannes
S. Iliadis
Affiliation:
University of Patras, Fatras, Greece
V. Tzannes
Affiliation:
University of Patras, Fatras, Greece
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This paper is concerned with topological spaces whose continuous maps into a given space R are constant, as well as with spaces having this property locally. We call these spaces R-monolithic and locally R-monolithic, respectively.

Spaces with such properties have been considered in [1], [5]-[7], [10], [11], [22], [28], [31], where with the exception of [10], the given space R is the set of real-numbers with the usual topology. Obviously, for a countable space, connectedness is equivalent to the property that every continuous real-valued map is constant. Countable connected (locally connected) spaces have been constructed in papers [2]-[4], [8], [9], [11]-[21], [23]-[26], [30].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 38 , Issue 6 , 01 December 1986 , pp. 1281 - 1298
Copyright
Copyright © Canadian Mathematical Society 1986

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