On a Class of Darboux Functions from a Topological Space to a Uniform Space
For a subset of the real line , Hattori space is a topological space whose underlying point set is the reals and whose topology is defined as follows: points from are given the usual Euclidean neighborhoods while remaining points are given the neighborhoods of the Sorgenfrey line. In this paper, among other things, we give conditions on which are sufficient and necessary for to be respectively almost Čech-complete, Čech-complete, quasicomplete, Čech-analytic and weakly separated (in...
Related to Shape Theory, in a previous paper (1992) we studied weak monomorphisms and weak epimorphisms in the category of pro-groups. In this note we give some intrinsic characterizations of the weak monomorphisms and the weak epimorphisms in pro-HTop* in the case when one of the two objects of such a morphism is a rudimentary system.