Extensions in bounded topology

Abstract

In a series of papers, Leseberg has studied and examined several fundamental aspects of generalized nearness in the realm of bounded topology. This paper deals with an alternate, detailed description of so-called bounded nearness and bounded topology by certain subdensity spaces and related maps. This type of spaces contains, in particular, b-near spaces as well as b-topological spaces in a nice fashion. Moreover, we found a one-to-one correspondence between suitable subdensity spaces and the related strict topological extensions. We point out that this newly established connection generalize the extensions which were studied by Bentley, Hušek, Ivanova, Ivanov, Lodato and Smirnov.