Convenient Topology

A new viewpoint of Topology, summarized under the name Convenient Topology, is considered in such a way that the structural deeciencies of topological and uniform spaces are remidied. This does not mean that these spaces are superruous. It means exactly that a better framework for handling problems of a topological nature is used. In this context semiuniform convergence spaces play an essential role. They include not only convergence structures such as topological structures and limit space structures, but also uniform convergence structures such as uniform structures and uniform limit space structures, and they are suitable for studying continuity, Cauchy continuity and uniform continuity as well as convergence structures in function spaces, namely simple convergence, continuous convergence and uniform convergence. Several results are presented which cannot be obtained by using topological or uniform spaces respectively.

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