On δ-ß-Separateness and strongly δ-ß-Connectedness and their applications.

The objective of the present paper is to study and investigate new notion of separated sets namely, δ-ß-Separated sets by using δ-ß- open sets. Moreover, with this notion we introduce new classes of connected spaces which are called strongly δ-ß-connected spaces and study some essential properties concerning of δ-ß- connected spaces. Several characterizations and fundamental properties concerning of such these classes of connected spaces with some δ-ß- Separtion axioms and compact spaces are obtained. The behavior of δ-ß- connected spaces with respect to several types of well-known mappings is discussed. Also, the digital spaces in the context of these new concepts are examined. Mathematics Subject Classification: 54B05, 54B10 ,54C10 ,54D18,90D42. [ABSTRACT FROM AUTHOR]