By Gerhard Preuß
A brand new beginning of Topology, summarized below the identify handy Topology, is taken into account such that a number of deficiencies of topological and uniform areas are remedied. this doesn't suggest that those areas are superfluous. It skill precisely greater framework for dealing with difficulties of a topological nature is used. during this environment semiuniform convergence areas play a necessary function. They comprise not just convergence constructions corresponding to topological buildings and restrict area constructions, but additionally uniform convergence buildings resembling uniform constructions and uniform restrict area buildings, and they're compatible for learning continuity, Cauchy continuity and uniform continuity in addition to convergence buildings in functionality areas, e.g. easy convergence, non-stop convergence and uniform convergence. quite a few attention-grabbing effects are offered which can't be acquired by utilizing topological or uniform areas within the ordinary context. The textual content is self-contained apart from the final bankruptcy, the place the intuitive proposal of nearness is included in handy Topology (there already exist first-class expositions on nearness spaces).