Dieter Leseberg

Subdensity as a convenient concept for Bounded Topology

The paper is published: Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. 69, 33 - 53 (2014/15)

MSC: 54A05   Topological spaces and generalizations (closure spaces, etc.)
  54B30   Categorical methods
  54C08   Weak and generalized continuity
  54D35   Extensions of spaces (compactifications, supercompactifications, completions, etc.)
  54E05   Proximity structures and generalizations

Abstract:   A subdensity space is a special case of a density space, which also occur under the name of hypernear space in [17]. Hence, most of classical spaces, like topological spaces, uniform spaces, proximity spaces, contiguity spaces or nearness spaces, respectively can be immediately described and studied in this general framework. Moreover, the more specific defined subdensity spaces allow us to consider and integrate the fundamental species of b- topological and b-near spaces, too, as presented and studied in [19]. In this paper it is shown that b-proximal spaces also can be involved, and b-topological spaces then have an alternate description by different corresponding subdensity spaces. At last, we establish a one-to-one correspondence between suitable subdensity spaces and their related strict topological extensions [1]. This relationship generalizes the one of LODATO, studied by him in the realm of generalized proximity spaces [20].

Keywords:   Bounded Topology; b-topological space; b-proximal space; strict topological extension
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