Proximal Lusternik-Schnirelmann, Császár and Bornology Categories

Peters J., VERGILI T., INAN E.

Fundamentals of contemporary mathematical sciences (Online), cilt.7, sa.2, ss.110-134, 2026 (TRDizin)

Özet

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.