| 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].