$ 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.