On Soft Topological Categories

Abstract

In this paper, we introduce the notion of a soft topological category as a natural consequence of the existence of topological category and soft category. Some examples of the soft topological categories are given. The properties of soft topological category are investigated and some important results are obtained. Also, the notion of topological functor is extended to the notion of soft topological functor. Finally, we present some examples about it.

Idealistic Soft Topological Hyperrings

“…Notice that a soft set over Ѡ can be regarded as a parameterized family of the subsets of the universeѠ. [15] The support of a soft set ( , ) is defined as a set…”

“…Successful results have been obtained using the soft set theory to solve complex problems in many fields such as economics, engineering, social sciences, medical science and others. Indeed, this theory has been applied with different perspectives in diverse areas such as algebra, topology, analysis and geometry by many mathematicians [10,11,12,13,14,15].…”

Soft Topological Transformation Groups

“…Recently, Oguz et al studied the actions of soft groups and obtained some important properties [8]. In addition, other algebraic properties of soft sets were studied in [9][10][11][12]. In the meantime, the pioneers of topological studies on soft sets are Shabir and Naz [13].…”

“…Later, Nazmul and Samanta presented the definition of a soft topological group [14]. Other than those, many topological studies have emerged [15][16][17][18][19][20][21][22][23][24].…”