Year: 2024
Type: article
Abstract: The main goal of the paper is to characterize families of [r,s]-(upper) superporous subsets of R, which generalize well-known notions of superporosity and strong superporosity of subsets of R. Definitions and properties of [r,s]-superporosity are symmetric to definitions and properties of superporosity and strong superporosity. The purpose in all cases is to define small subsets of the line using the notion of porosity. Superporous sets preserve positive porosity, and strongly superporous sets preserve strong porosity; i.e., if E is superporous (correspondingly, E is strongly superporous), then for every x∈E and for every F such that porosity of F at x is greater than 0 (correspondingly, is equal to 1), porosity of E∪F at x is greater than 0 (correspondingly, is equal to 1). Taking arbitrary positive porosity, instead of 0 or 1, we obtain the symmetric definition as follows: [r,s]-superporosity for 0
Source: Symmetry
DOI: 10.3390/sym17010011
Authors: Stanisław Kowalczyk, Małgorzata Turowska
Institution: Uniwersytet Pomorski w Słupsku
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,728
OpenAlex ID: W4405781620