Abstract
The aim of the present study is to introduce the concept of soft topological transformation groups by examining the topological transformation groups, which are the core subject of algebraic topology under the soft approach. Actions of soft topological groups on soft topological spaces are studied, and the category of soft topological transformation groups is constructed. Also, a translation and conjugation of the soft topological groups are described. Finally, the definitions of soft orbit spaces and soft homogeneous spaces are given, and some of the properties of these concepts are examined in detail.
Highlights
IntroductionTopology and algebra are two main areas of mathematics that play complementary roles
Topology and algebra are two main areas of mathematics that play complementary roles.Topology deals with continuity and convergence, while algebra examines all kinds of operations. these two areas tend to develop independently, they are in a natural interaction with other areas of mathematics such as functional analysis, representation theory, dynamical systems.In particular, most of the important objects of mathematics contain a blend of topological and algebraic structures
These two areas tend to develop independently, they are in a natural interaction with other areas of mathematics such as functional analysis, representation theory, dynamical systems
Summary
Topology and algebra are two main areas of mathematics that play complementary roles. The study of topological transformation groups were originated in the work of Montgomery and Zippin, which contains a solution of Hilbert’s fifth problem [1]. This subject has reached a wide range of study potential and continues to be one of the most dominant topics in mathematics nowadays [2]. Researches based on the soft set theory continues to develop rapidly in many fields such as engineering, medicine, economics, environmental sciences In recent years, this theory has been combined with some important mathematical theories such as algebra and topology.
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