$ S $-$ \delta $-connectedness in $ S $-proximity spaces

Abstract

New types of connectedness in $ S $-proximity spaces, named as an $ S $-$\delta$-connectedness, local $ S $-$ \delta $-connectedness are introduced. Also, their inter-relationships are studied. In an $ S $-proximity space $ (X, \delta_{X}) $, the $ S $-$ \delta $-connectedness of a subset $ U $ of $ X $ with respect to $ \delta_{X} $ may not be same as the $ S $-$ \delta $-connectedness of $ U $ with respect to its subspace proximity $ \delta_{U} $. Further, $ S $-$ \delta $-component and $ S $-$ \delta $-treelike spaces are also defined and a number of results are given.