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Under what may be thought of as a guise of a description of pathology are indicated here certain ways in which Cech completeness, ArhangeΓskii's p-space concept, and metacompactness enlarge on the respective concepts of metric absolute Gs's, metrizability, and paracompactness. This is done through examination of certain aspects of the theory of multivalued mappings. It is taken as a point of orientation that the topic of Tychonoff locally bicompact spaces has a substantial mathematicaldoi:10.2140/pjm.1969.30.555 fatcat:ncoggg25wjcivpmqdbagtnpcr4