On the Possibility of N-Topological Spaces

Authors: Kamran Alam Khan

The notion of a bitopological space as a triple (X,I_1,I_2), where X is a set and I_1and I_2are topologies on X, was first formulated by J.C.Kelly [5]. In this paper our aim is to introduce and study the notion of an N-topological space (X,I_1,I_2,………I_N). We first generalize the notion of an ordinary metric to n variables. This metric will be called K-metric. Then the notion of a quasi-pseudo-K-metric will be introduced. We then follow the approach of Kelly to introduce and study the notion of an N-topological space. An example for such a space is produced using chain topology. And finally we define and study some of the possible separation properties for N-topological spaces.

Comments: 4 Pages. Published in International Journal of Mathematical Archive (IJMA)

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[v1] 2013-06-21 08:24:13

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