Connectedness of Soft r-Topological Spaces

Topological properties are essential for developing digital line spaces and computer graphics other than the field of topology. Soft topological properties must play an equal role as classical topological properties or even better. Soft connectedness is one of the most fundamental soft topological aspects. It studies the nearness of two objects from a topological point of view. By considering the significance of this concept, we make this contribution to study the connectedness of some strong soft topologies. We begin by introducing a new class of soft open sets, named soft r-open sets, followed by establishing its main properties. We show that the collection of all soft r-open sets constitutes a soft topology, which is coarser than the original one. Then, we define the concept of soft r-separated sets, which helps us to give the r-connectedness of a soft set. We show that soft connectedness implies soft r-connectedness, which implies soft 𠜃-connectedness of a soft set. Counterexamples are provided to show that the implications are not reversible. However, they are identical on a soft open set. Further properties and characterizations of soft r-connected sets are proposed.