Convergence space, cauchy space, convergence semigroup, cauchy semigroup, continuous action, cauchy continuous action, compactification, completion, pseudoquotients
Given a convergence space X, a continuous action of a convergence semigroup S on X and a compactification Y of X, under what conditions on X and the action on X is it possible to extend the action to a continuous action on Y . Similarly, given a Cauchy space X, a Cauchy continuous action of a Cauchy semigroup S on X and a completion Y of X, under what conditions on X and the action on X is it possible to extend the action to a Cauchy continuous action on Y . We answer the first question for some particular compactifications like the one-point compactification and the star compactification as well as for the class of regular compactifications. We answer the second question for the class of regular strict completions. Using these results, we give sufficient conditions under which the pseudoquotient of a compactification/completion of a space is the compactification/completion of the pseudoquotient of the given space
Doctor of Philosophy (Ph.D.)
College of Sciences
Length of Campus-only Access
Doctoral Dissertation (Open Access)
Dissertations, Academic -- Sciences, Sciences -- Dissertations, Academic
Losert, Bernd, "Extensions Of S-spaces" (2013). Electronic Theses and Dissertations. 2653.