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Acta Mathematica Hungarica

, Volume 158, Issue 1, pp 1–16 | Cite as

The regular topology on C(X, Y)

  • A. Jindal
  • V. JindalEmail author
Article
  • 79 Downloads

Abstract

This paper studies the metrizability and various completeness properties of the space Cr(X,Y), where Y is a metric space containing a nontrivial path and Cr(X,Y) denotes the space of all continuous functions from a Tychonoff space X to Y, equipped with the regular topology.

Mathematics Subject Classification

primary 54C35 secondary 54D05 54E18 54E35 54E50 54E99 

Key words and phrases

regular topology metrizability uniformly complete completely metrizable Čech-complete sieve-complete partition-complete 

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Notes

Acknowledgement

The authors would like to thank the referee for the careful reading of the manuscript and for giving many useful suggestions that led to a number of improvements to the original version of this paper.

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology JammuJammuIndia
  2. 2.Department of MathematicsMalaviya National Institute of Technology JaipurJaipurIndia

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