Golam biswas - Academia.edu (original) (raw)

Papers by Golam biswas

New Mathematics and Natural Computation, Jun 30, 2023

In this paper, our prime aim is to develop the concept of fundamental group structure in soft set... more In this paper, our prime aim is to develop the concept of fundamental group structure in soft set theoretic approach. To execute this, first, we have defined soft homotopy of maps, soft path, soft loop, soft path homotopy, soft loop homotopy, product of soft loops, soft homotopy class, etc., at a soft element using generalized soft mappings and their important behaviors are studied. Finally, we have introduced the notion of fundamental group whose members are soft homotopy classes. Some examples are also discussed in different soft topological spaces.

Research Square (Research Square), Jun 5, 2023

In this communication, we aimed to construct a non-trivial fundamental group of soft homotopy cla... more 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, S 1. Finally, applying the above concepts, a proof of Brouwer's fixed point theorem is established in soft set setting.

In this communication, we aimed to construct a non-trivial fundamental group of soft homotopy cla... more 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.

New Mathematics and Natural Computation

New Mathematics and Natural Computation, Jun 30, 2023

In this paper, our prime aim is to develop the concept of fundamental group structure in soft set... more In this paper, our prime aim is to develop the concept of fundamental group structure in soft set theoretic approach. To execute this, first, we have defined soft homotopy of maps, soft path, soft loop, soft path homotopy, soft loop homotopy, product of soft loops, soft homotopy class, etc., at a soft element using generalized soft mappings and their important behaviors are studied. Finally, we have introduced the notion of fundamental group whose members are soft homotopy classes. Some examples are also discussed in different soft topological spaces.

Research Square (Research Square), Jun 5, 2023

In this communication, we aimed to construct a non-trivial fundamental group of soft homotopy cla... more 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, S 1. Finally, applying the above concepts, a proof of Brouwer's fixed point theorem is established in soft set setting.

In this communication, we aimed to construct a non-trivial fundamental group of soft homotopy cla... more 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.

New Mathematics and Natural Computation