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A quasitopos containing CONV and MET as full subcategories. (English) Zbl 0672.54003

The category of convergence-approach spaces with contractions (CAP) is defined and shown to be a quasitopos. The authors determine the way in which several interesting categories related to convergence and distance are embedded in CAP. For example, the category of approach spaces with the contractions is a bireflective subcategory and the category of convergence spaces with continuous maps is a full subcategory.
Reviewer: A.J.Klein

MSC:

54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
54B30 Categorical methods in general topology
18B25 Topoi
54E35 Metric spaces, metrizability
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