Existence of a homeomorphism from the space of continuous functions to the space of compact Subsets of a topological space, X

Published

23-08-2024

DOI:

https://doi.org/10.58414/SCIENTIFICTEMPER.2024.15.3.09

Keywords:

hyperspace, regular, compact-open topology, point wise convergence topology

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Issue

Section

SECTION B: PHYSICAL SCIENCES, PHARMACY, MATHS AND STATS

Authors

  • Amalraj . P Department of Mathematics, Sanatana Dharma College, Alappuzha, Rajagiri School of Engineering and Technology, APJ Abdul Kalam Technological University, Kerala, India.
  • Vinodkumar P. B. Centre for Topology and Applications, Department of Mathematics, Rajagiri School of Engineering and Technology, Cochin, Kerala, India.

Abstract

This paper presents proof that there exists a subspace of the space of continuous functions on a topological space X, which is homeomorphic to the space of compact subsets of X. Those let C(X) denote the space of continuous functions on a topological space X and K(X) be the space of compact subsets of X. We prove that there exists a subspace of C(K(X)) which is homeomorphic to C(X). The result remains valid for compact open topology and point-wise convergence topology on K(X).

How to Cite

Amalraj . P, & Vinodkumar P. B. (2024). Existence of a homeomorphism from the space of continuous functions to the space of compact Subsets of a topological space, X. The Scientific Temper, 15(03), 2470–2472. https://doi.org/10.58414/SCIENTIFICTEMPER.2024.15.3.09

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