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Metrizability and Completeness Properties of \(C_{\tau } (X, Y)\) for \(\tau = d,f, g\)

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

Abstract

In this chapter, we study various topological 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 metric space Y. In particular, we study the metrizability, first countability and various completeness properties of the uniform, fine and graph topologies on C(XY).

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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