Abstract
It is the aim of this paper to compare the Scott topology and other related function space topologies with the limitierung of continuous convergence and to make the intrinsic connections to well-known results of J. Isbell and B. Banaschewski clearly visible. The main point about the limitierung of continuous convergence is: whenever it is a topology, then it is the “right” function space topology. The people main working categories are the limit spaces and the topological spaces. For the convenience of the reader, the people record first some basic notions and facts on convergence categories, in particular, concerning the limitierung of continuous convergence. There is a nice characterization of splitting and conjoining topologies via continuous convergence.
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