Dieter Leseberg

Improved nearness research II

The paper is published: Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. 66, 87 - 102 (2011)

MSC: 54A05   Topological spaces and generalizations (closure spaces, etc.)
  54B30   Categorical methods [See also 18B30]
  54D35   Extensions of spaces (compactifications, supercompactifications, completions, etc.)
  54E17   Nearness spaces

Abstract:   When applying in consequence the new created concept ''Bounded Topology'' \cite{les8} hence ''classical structures'' like nearness structures \cite{les5}, convergence structures \cite{les8} and syntopogenous structures \cite{les8} will be analyzed in connexion with neighbourhood structures \cite{les11} or supertopologies \cite{les4}, respectively.
In this context ''nearness'' is presented as special paranearness, ''convergence'' as special $b$-convergence and being ''syntopogenous'' as special case of $b$-syntopogenous, leading us accordingly to a \underline{general} theory of his \underline{own}!
Now, in this paper we will study certain superclan spaces, whichever are in one-to-one correspondence to \underline{strict} topological extensions. Here, we should mention that the presented concept is \underline{not} of \underline{utmost} generality, but then the reader is referred to \cite{les9}.

Keywords:   LEADER proximity; supertopological space; LODATO space; supernear space; superclan space; Bounded Topology
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