Date of Award
Doctor of Philosophy (PhD)
Professor R. G. Lintz
This thesis deals with paracompact spaces with the covering dimension of Lebesgue. A paracompact Hausdorff space with finite covering dimension is characterized by sequences of covers, as an inverse limit of finite dimensional metric spaces, and in terms of a single finite dimensional metric space. In connection with non-deterministic mathematics we introduce the modeling distribution and it is proved (under suitable assumptions) that a modeling distribution preserves paracompactness, complete paracompactness, strong paracompactness, compactness, and final compactness, and lowers covering dimension.
Mogyorosy, Joseph, "Covering Dimension and the Modeling Distribution" (1975). Open Access Dissertations and Theses. Paper 860.