Strong Whitney and strong uniform convergences on a bornology

• Published in: Journal of mathematical analysis and applications Vol. 505; no. 1; p. 125634
• Main Authors: Chauhan, Tarun Kumar, Jindal, Varun
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.01.2022
• Subjects: Bornology; Continuous convergence; Exhaustive net; Shielded from closed sets; Strong uniform convergence; Strong Whitney convergence; Strong Whitney convergence; Bornology; Continuous convergence; Shielded from closed sets; Strong uniform convergence; Exhaustive net
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2021.125634

For any two metric spaces (X,d), (Y,ρ) and a bornology B on X, we study the relationship between strong uniform convergence (introduced by Beer and Levi in [8]) and strong Whitney convergence (introduced by A. Caserta in [15]) on B on YX (and C(X,Y)). The relationships of these convergences with their classical counterparts, that is, Whitney and uniform convergences on B are also considered. Moreover, for any two bornologies B and B′ on X, we examine the relationship between strong Whitney (strong uniform) convergence on B′ and Whitney (uniform) convergence on B. Finally, we investigate the relation of strong Whitney convergence with the well-known continuous convergence of nets of functions.