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Connectedness and Path Connectedness of \(C_{\tau }(X, Y)\) for a Normed Linear Space Y, Where \(\tau = d, f, g\)

  • Robert A. McCoyEmail author
  • Subiman Kundu
  • Varun Jindal
Chapter
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Abstract

In this chapter, we study the connectedness and some related algebraic properties of the uniform, fine and graph topologies on the space C(XY), the set of all continuous functions from a Tychonoff space X to a normed linear space \((Y,||\cdot ||)\). We show that these function spaces are in general not connected and in that case we determine the components and path components of these spaces.

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Department of MathematicsVirginia Polytechnic Institute and State UniversityBlacksburgUSA
  2. 2.Department of MathematicsIndian Institute of Technology DelhiNew DelhiIndia
  3. 3.Department of MathematicsMalaviya National Institute of TechnologyJaipurIndia

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