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 potential precisely greater framework for dealing with difficulties of a topological nature is used. during this atmosphere semiuniform convergence areas play a vital function. They comprise not just convergence buildings akin to topological constructions and restrict area buildings, but in addition uniform convergence buildings reminiscent of uniform buildings and uniform restrict area constructions, and they're compatible for learning continuity, Cauchy continuity and uniform continuity in addition to convergence constructions in functionality areas, e.g. basic convergence, non-stop convergence and uniform convergence. quite a few fascinating effects are provided which can't be got through the use of topological or uniform areas within the ordinary context. The textual content is self-contained except for the final bankruptcy, the place the intuitive idea of nearness is included in handy Topology (there already exist first-class expositions on nearness spaces).
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