<abstract xmlns="http://www.w3.org/1999/xhtml"><p>. A notion of <italic>AI </italic>-topology, a generalization of Wilczy´nski’s <italic>I</italic>-density topology (see [Wilczy´nski, W.: <italic>A generalization of the density topology</italic>, Real. Anal. Exchange <bold>8 </bold>(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 <italic>Ad</italic>- -density topology on the real line given in [Wojdowski, W.: <italic>A generalization of</italic><italic>density topology</italic>, Real. Anal. Exchange <bold>32 </bold>(2006/2007), 1-10]. We also discuss the properties of continuous functions with respect to the topology.</p></abstract>

. A notion of AI -topology, a generalization of Wilczy´nski’s I-density topology (see [Wilczy´nski, W.: A generalization of the density topology, Real. Anal. Exchange 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 Ad- -density topology on the real line given in [Wojdowski, W.: A generalization ofdensity topology, Real. Anal. Exchange 32 (2006/2007), 1-10]. We also discuss the properties of continuous functions with respect to the topology.

A category analogue of the generalization of Lebesgue density topology

Institute of Mathematics Technical University of Łódź Wólczánska 215 PL–90-924 Łódź POLAND

Tatra Mountains Mathematical Publications

{"article-title":"A category analogue of the generalization of Lebesgue density topology"}

. A notion of AI -topology, a generalization of Wilczy´nski’s I-density topology (see [Wilczy´nski, W.: A generalization of the density topology, Real. Anal....

A category analogue of the generalization of Lebesgue density topology

Publié en ligne: 12 nov. 2012

Pages: 11 - 25

DOI: https://doi.org/10.2478/v10127-009-0002-0

Mots clés
density point, density topology.

This content is open access.

A category analogue of the generalization of Lebesgue density topology

Publié en ligne: 12 nov. 2012

Pages: 11 - 25

DOI: https://doi.org/10.2478/v10127-009-0002-0

Mots clésdensity point, density topology.

This content is open access.

Mots clés
density point, density topology.