Author(s)

Dieter Leseberg^*

Institut für Mathematik, Freie Universitat, Berlin, Germany.

In the realm of Bounded Topology we now consider supernearness spaces as a common generalization of various kinds of topological structures. Among them the so-called Lodato spaces are of significant interest. In one direction they are standing in one-to-one correspondence to some kind of topological extensions. This last statement also holds for contiguity spaces in the sense of Ivanova and Ivanov, respectively and moreover for bunch-determined nearness spaces as Bentley has shown in the past. Further, Do?tch?nov proved that the compactly determined Hausdorff extensions of a given topological space are closely connected with a class of supertopologies which he called b-supertopologies. Now, the new class of supernearness spaces—called paranearness spaces—generalize all of them, and moreover its subclass of clan spaces is in one-to-one correspondence to a certain kind of symmetric strict topological extension. This is leading us to one theorem which generalize all former mentioned.

Set-Convergence, Supertopological Space, Lodato Space, Contiguity Space, Nearness, Paranearness

Leseberg, D. (2014) Improved Nearness Research. Advances in Pure Mathematics, 4, 610-626. doi: 10.4236/apm.2014.411070.