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Improved Nearness Research

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DOI: 10.4236/apm.2014.411070    2,675 Downloads   3,032 Views   Citations
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ABSTRACT

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

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

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