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Preliminaries

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

Abstract

Let C(XY) denote the set of all continuous functions from a topological space X to a topological space Y. When \(Y= \mathbb {R}\), the set of all real numbers, equipped with the usual distance metric, we write C(X) instead of \(C(X,\mathbb {R})\). Firstly, we give the definitions of the uniform, fine and graph topologies on the set C(XY). Then we compare these topologies among themselves and with the point-open and compact-open topologies on C(XY) for a metric space (Yd). In the last section, we study the dependence of the uniform and fine topologies upon the choice of a compatible metric on Y.

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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