Connectedness Properties

Gerhard Preuss
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Gerhard Preuss: Freie Universität Berlin, Institut für Mathematik I

Chapter Chapter 5 in Foundations of Topology, 2002, pp 161-179 from Springer

Abstract: 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 2 Δ 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 2 Δ is constant.

Keywords: Topological Space; Usual Sense; Uniform Space; Connected Subset; Dense Subspace (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1007/978-94-010-0489-3_6

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