Covering Dimension and the Modeling Distribution

Abstract

<p>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.</p>