Journal of Emerging Trends in Engineering and Applied Sciences: Research Areas

Article Title: Establishment the Relationship between Topological Space and Normal Sub-group and Continuous Function for Topological Sense and Metrical Sense
by Suman Chandra Paul, Md Sohel Rana, Saiful Islam, Md. Habibul Bashar Bangabandhu Sheikh Mujibur Rahman

Abstract:
In this paper we continue the study with the relation between topological space and normal subgroup by introducing the notion of basic concepts and properties of topological space and normal subgroup. We have established the relation between compact sets and normal subgroup; base and normal subgroup; topological space and normal subgroup. Also some basic definitions, relations, theorems and examples are expressed. Topological space is relevant to physics in areas such as condensed matter physics, quantum field theory and physical cosmology. Also, knot theory, a branch of topology, is used in biology. Due to these types of application of topology we have tried to establish some relations and a theorem by using topological space and metric space. The definition of the continuous function for the case of metric space coincides with the definition of the continuous function in the sense of topological space. This relation will be helped to develop the relation between metric space and topological space which will be used for developing networking system.

Keywords: topological space, normal subgroup, metric space, continuous function of metric space, neighbourhood

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