| 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}.