Soft version of compact and Lindelöf spaces using soft somewhere dense sets

Abstract

Herein, we applied soft somewhere dense sets to initiate six sorts of soft spaces called almost (nearly, mildly) soft SD-compact and almost (nearly, mildly) soft SD-Lindelöf spaces. We study the master properties of these spaces and illustrate the relations between them with the help of examples. In addition, we clarify that the six soft spaces are equivalent under a soft SD-partition. Moreover, the relationships between the initiated spaces and enriched soft topological spaces and other well-known spaces such as soft S-connected are indicated.

Keywords

• soft somewhere dense set
• soft cs-dense set
• almost soft sd-compact
• almost soft sd-lindelöf
• nearly soft sd-compact
• nearly soft sd-lindelöf
• mildly soft sd-compact
• mildly soft sd-lindelöf