DOI: 10.54974/fcmathsci.1703891 ISSN: 2717-6185

Proximal Lusternik-Schnirelmann, Császár and Bornology Categories

James F. Peters, Tane Vergili, Ebubekir İnan
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This paper introduces new forms of proximity space categories, namely, proxLS and dproxLS, spatial and descriptive proximity refinements of the Lusternik-Schnirelmann category LS and desProx, which is a descriptive proximity extension of the Császár Prox category. A main result given here is that a proximity space (X, δ) is proximally contractible if and only if the proximal Lusternik-Schnirelmann category LSδ(X) = 1. Several other results are also given, namely, Prox has all nonempty products and coproducts and ProxBor has all nonempty coproducts.

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