Abstract:We study \v Cech complete and strongly \v Cech complete topological spaces, as well as extensions of topological spaces having these properties. Since these two types of completeness are defined by means of covering properties, it is quite natural that they should have a convenient formulation in the setting of nearness spaces and that in that setting these formulations should lead to new insights and results. Our objective here is to give an internal characterization of (and to study) those nearness structures which are induced by topological extensions of the two above mentioned types.
Keywords: \v Cech complete, strongly \v Cech complete, nearness space
AMS Subject Classification: 54E17, 54D20, 54B30, 54D30