A category analogue of the generalization of Lebesgue density topology

Rok, strany: 2009, 11 - 25

A notion of $\mathcal{A}_{I}$-topology, a generalization of Wilczy\'{n}\-ski's $I$-density topology (see [Wilczy\'{n}ski, W.: \textit{A generalization of the density topology}, Real. Anal. Exchange \textbf{8} (1982-1983), 16--20] is introduced. The notion is based on his reformulation of the definition od Lebesgue density point. We consider a category version of the topology, which is a category analogue of the notion of an $\mathcal{A}_{d}$\discretionary{-}{-}{-}density topology on the real line given in [Wojdowski, W.: \textit{A generalization of density topology}, Real. Anal. Exchange \textbf{32} (2006/2007), 1--10]. We also discuss the properties of continuous functions with respect to the topology.

ISO 690:

Wojdowski, W. 2009. A category analogue of the generalization of Lebesgue density topology. In Tatra Mountains Mathematical Publications, vol. 42, no.1, pp. 11-25. 1210-3195.

APA:

Wojdowski, W. (2009). A category analogue of the generalization of Lebesgue density topology. Tatra Mountains Mathematical Publications, 42(1), 11-25. 1210-3195.