Vol.1 , No. 4, Publication Date: Jun. 29, 2015, Page: 174-179

[1] | G. A. Kamel, Department of Mathematics, Faculty of Science, Fayoum University, Fayoum, Egypt. |

Although, there are lots of equivalent ways of formulating for computing the number of topological spaces in finite set. In this paper, we formulated special case for computing the number of chain topological spaces, and maximal elements with the natural generalization. We look at the concept of partial chain topologies on finite set with respect to the given subset. We determine the number of partial chain topologies with k open sets, and so the number of all chain topologies on finite set will be outlined. To support our study, some examples, and properties of this concept will be studied. Moreover, we determine the rule for computing the number of all maximal elements in the set of all chain topologies.

Keywords

Chain Topology, Partial Chain Topology, Number of Chain Topologies on Finite Set, Maximal Elements in Chain Topologies

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