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Generalized quotient topologies and hereditary classes

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Abstract

We introduce a definition of \({\pi}\) being injective with respect to a generalized topology and a hereditary class where \({\pi}\) is a generalized quotient map between generalized topological spaces. This definition is mainly a sufficient condition to show several relations about a generalized topology and its induced generalized quotient topology when either is extended by a hereditary class or it can be regarded as an extension of a generalized topology via a hereditary class.

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  1. Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok, 10330, Thailand

    P. Montagantirud & S. Phonrakkhet

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  1. P. Montagantirud
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  2. S. Phonrakkhet
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Correspondence to P. Montagantirud.

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Montagantirud, P., Phonrakkhet, S. Generalized quotient topologies and hereditary classes. Acta Math. Hungar. 161, 1–15 (2020). https://doi.org/10.1007/s10474-020-01039-0

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  • DOI: https://doi.org/10.1007/s10474-020-01039-0

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