<abstract xmlns="http://www.w3.org/1999/xhtml">We present a further generalization of the <italic>𝒯AI</italic>-density topology introduced in [W. Wojdowski, <italic>A category analogue of the generalization of Lebesgue density topology,</italic> Tatra Mt. Math. Publ. <bold>42</bold> (2009), 11–25] as a generalization of the <italic>I</italic>-density topology. We construct an ascending sequence {𝒯<italic>A</italic><italic>I</italic>(<italic>n</italic>)}<italic>n</italic>∈ℕ of density topologies which leads to the 𝒯<italic>A</italic><italic>I</italic>(ω)-density topology including all previous topologies. We examine several basic properties of the topologies.</abstract>

We present a further generalization of the 𝒯AI-density topology introduced in [W. Wojdowski, A category analogue of the generalization of Lebesgue density topology, Tatra Mt. Math. Publ. 42 (2009), 11–25] as a generalization of the I-density topology. We construct an ascending sequence {𝒯AI(n)}n∈ℕ of density topologies which leads to the 𝒯AI(ω)-density topology including all previous topologies. We examine several basic properties of the topologies.

On Generalization of the <italic>𝒯AI</italic>-Density Topology

Tatra Mountains Mathematical Publications

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On Generalization of the -Density Topology

We present a further generalization of the 𝒯AI-density topology introduced in [W. Wojdowski, A category analogue of the generalization of Lebesgue density...

On Generalization of the 𝒯_{A_I}-Density Topology

Published Online: Nov 18, 2017

Page range: 29 - 45

Received: Dec 11, 2015

DOI: https://doi.org/10.1515/tmmp-2017-0003

Keywords
density point, density topology

© 2017 Alicja Krzeszowiec et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On Generalization of the 𝒯AI-Density Topology

Published Online: Nov 18, 2017

Page range: 29 - 45

Received: Dec 11, 2015

DOI: https://doi.org/10.1515/tmmp-2017-0003

Keywordsdensity point, density topology

© 2017 Alicja Krzeszowiec et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On Generalization of the 𝒯_{A_I}-Density Topology

Keywords
density point, density topology