On continuous mappings of metacompact Čech complete spaces

Under what may be thought of as a guise of a description of pathology are indicated here certain ways in which Cech completeness, Arhangeskii'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 mathematical interest. It is assumed obvious that such spaces are locally paracompact p-spaces. An underlying point of view is that the class of regular locally paracompact ^-spaces extends along natural lines the class of regular locally metrizable spaces.