Abstract
A topological space X = (X, X) is connected iff each continuous map f :X → D2 from X into the two-point discrete topological space D2 is constant. This characterization of the usual concept of connectedness leads to an analogous definition of connectedness for topological constructs, since two-point discrete objects are available, e.g. if D Δ2 denotes the two-point discrete uniform space, then a uniform space X = (X, W) is called ‘connected’ (or more exactly: uniformly connected) iff each uniformly continuous map f :X → D Δ2 is constant.
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© 2002 Springer Science+Business Media Dordrecht
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Preuss, G. (2002). Connectedness Properties. In: Foundations of Topology. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0489-3_6
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DOI: https://doi.org/10.1007/978-94-010-0489-3_6
Publisher Name: Springer, Dordrecht
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