Closure operators in convergence approach spaces

Authors: MUHAMMAD QASIM, MEHMET BARAN, HASSAN ABUGHALWA

Abstract: In this paper, we characterize closed and strongly closed subsets of convergence approach spaces and introduce two notions of closure in the category of convergence approach spaces which satisfy idempotent, productive and (weakly) hereditary properties. Furthermore, we explicitly characterize each of $T_{i}$ convergence approach spaces, $i=0,1,2$ with respect to these closure operators and show that each of these subcategories of $T_{i}$ convergence approach spaces, $i=0,1,2$ are epireflective as well as we investigate the relationship among these subcategories. Finally, we characterize connected convergence approach spaces.

Keywords: Convergence approach space, topological category, closure operators, connectedness, initial lift, final lift

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