${\mathcal I}$-Density Continuous Functions

Download or read book ${\mathcal I}$-Density Continuous Functions written by Krzysztof Ciesielski and published by American Mathematical Soc.. This book was released on 1994 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: The [script capital]I-density topology is a generalization of the ordinary density topology to the setting of category instead of measure. This work involves functions which are continuous when combinations of the [script capital]I-density, deep [script capital]I-density, density and ordinary topology are used on the domain and range. In the process of examining these functions, the [script capital]I-density and deep-[script capital]I-density topologies are deeply explored and the properties of these function classes as semigroups are considered.