Abstract
We give various relations between lower (upper) semi-continuous functions and cliquish functions in a generalized topological space. Also, we answer the open problems raised by Korczak-Kubiak et al. in [5].
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References
Borsik, J.: Points of generalized continuities. Tatra Mt. Math. Publ. 52, 153–160 (2012)
Császár, Á.: Generalized open sets. Acta Math. Hungar. 75, 65–87 (1997)
Császár, Á.: Remarks on quasi-topologies. Acta Math. Hungar. 119, 197–200 (2008)
Ekici, E.: Generalized hyperconnectedness. Acta Math. Hungar. 133, 140–147 (2011)
Korczak-Kubiak, E., Loranty, A., Pawlak, R.J.: Baire generalized topological spaces, generalized metric spaces and infinite games. Acta Math. Hungar. 140, 203–231 (2013)
Li, Z., Lin, F.: Baireness on generalized topological spaces. Acta Math. Hungar. 139, 320–336 (2013)
Min, W.K.: Some results on generalized topological spaces and generalized systems. Acta Math. Hungar. 108, 171–181 (2005)
Vadakasi, S., Renukadevi, V.: Properties of nowhere dense sets in GTSs. Kyungpook Math. J. 57, 199–210 (2017)
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The authors are very grateful to the reviewer for their careful and meticulous reading of the paper.
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Renukadevi, V., Vadakasi, S. On lower and upper semi-continuous functions. Acta Math. Hungar. 160, 1–12 (2020). https://doi.org/10.1007/s10474-019-01013-5
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DOI: https://doi.org/10.1007/s10474-019-01013-5
Key words and phrases
- nowhere dense
- strongly nowhere dense
- Baire space
- lower (upper) semi-continuous function
- cliquish function