Existence of a homeomorphism from the space of continuous functions to the space of compact Subsets of a topological space, X
Year: 2024
Type: article
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).
Source: THE SCIENTIFIC TEMPER
Authors: Amalraj . P, Vinodkumar P. B.
Institution: APJ Abdul Kalam Technological University
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4403140448