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Mathematics > General Topology

arXiv:2202.02023 (math)
[Submitted on 4 Feb 2022]

Title:Cardinal Functions, Bornologies and Strong Whitney convergence

Authors:Tarun Kumar Chauhan, Varun Jindal
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Abstract:Let $C(X)$ be the set of all real valued continuous functions on a metric space $(X,d)$. Caserta introduced the topology of strong Whitney convergence on bornology for $C(X)$ in [A. Caserta, Strong Whitney convergence, Filomat, 2012], which is a generalization of the topology of strong uniform convergence on bornology introduced by Beer-Levi in [Beer-Levi, Strong uniform continuity, J. Math. Anal. Appl., 2009]. The purpose of this paper is to study various cardinal invariants of the function space $C(X)$ endowed with the topologies of strong Whitney and Whitney convergence on bornology. In the process, we present simpler proofs of a number of results from the literature. In the end, relationships between cardinal invariants of strong Whitney convergence and strong uniform convergence on $C(X)$ have also been studied.
Comments: 17 Pages
Subjects: General Topology (math.GN)
Cite as: arXiv:2202.02023 [math.GN]
  (or arXiv:2202.02023v1 [math.GN] for this version)
  https://doi.org/10.48550/arXiv.2202.02023

Submission history

From: Varun Jindal [view email]
[v1] Fri, 4 Feb 2022 08:53:24 UTC (222 KB)
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