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Fundamental Group of Soft Homotopy Classes of Unit Circle and Its Application
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Abstract
In this communication, we aimed to construct a non-trivial fundamental group of soft homotopy classes and to find out its application. To achieve this, firstly we have defined soft exponential mappings, soft lift of a continuous soft mapping. Moreover, the relationship among some important properties such as soft path lifting property, soft homotopy lifting property, etc. is discussed. We also constructed the fundamental group of soft homotopy classes of unit circle, S1. Finally, applying the above concepts, a proof of Brouwer’s fixed point theorem is established in soft set setting.
2010 Mathematics Subject Classification:
14H30, 14H99, 20F34, 06D72, 55Q99.
Title: Fundamental Group of Soft Homotopy Classes of Unit Circle and Its Application
Description:
Abstract
In this communication, we aimed to construct a non-trivial fundamental group of soft homotopy classes and to find out its application.
To achieve this, firstly we have defined soft exponential mappings, soft lift of a continuous soft mapping.
Moreover, the relationship among some important properties such as soft path lifting property, soft homotopy lifting property, etc.
is discussed.
We also constructed the fundamental group of soft homotopy classes of unit circle, S1.
Finally, applying the above concepts, a proof of Brouwer’s fixed point theorem is established in soft set setting.
2010 Mathematics Subject Classification:
14H30, 14H99, 20F34, 06D72, 55Q99.
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