Approach merotopological spaces and their completion (Q978992)

The authors introduce the concept of approach merotopological spaces and demonstrate that the resulting construct \textbf{AMT} is topological and contains the constructs \textbf{TOP} of topological spaces, \textbf{MET} of metric spaces, \textbf{AP} of approach spaces, \textbf{AMER} of approach merotopological spaces, \textbf{ANEAR} of approach nearness spaces, and \textbf{MERTOP} of merotopological spaces as subconstructs. In particular, \textbf{TOP} and \textbf{MERTOP} are simultaneously bicoreflective and bireflective full subconstructs of \textbf{AMT}. Moreover, they construct a bunch completion of an approach merotopological space, introduce the concept of regularity, and show that for regular approach nearness spaces the cluster completion can be obtained as a retract of its bunch completion.