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Abstract
Preservation of properties under continuous functions on topological spaces is a very important tool for the classification of topological spaces. However, in some cases the quaiscontinuous functions are more useful than the continuous functions for classifying topological spaces. In this paper, we study preservation of strong forms of connectedness under quasicontinuous function that help to prove the general form of intermediate value theorem.
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References
- Abd EI-Monsef, M.E., Mahmoud, R.A., and El-Deeb, S.N., “β-open sets and β-continuous mappings”, Bull. Fac. Sci. Assiut Univ 1983; 12(1): 77-90.
- Andrijevi, D., “On B-open Sets”, Matematiki Vesnik 1996; 48: 59-64. doi:http://eudml.org/doc/252912
- Baire, R., “Sur les fonctions de variables reelles”, Annali di Matematica Pura ed Applicata 1899; 3(1):1-123. doi:10.1007/BF02419243
- Ekici, E., “On separated sets and connected spaces”, Demonstratio Math 2007; 40(1): 209-217. doi:10.1515/dema-2007-0122
- Jafari, S. and Noiri, T., “Properties of β-connected spaces”, Acta Mathematica Hungarica 2003; 101(3): 227-236. doi:10.1023/B:AMHU.0000003907.90823.79
- Kempisty, S., “Sur les fonctions quasicontinues”, fundamenta Mathematicae 1932; 1: 184-197. doi:http://matwbn.icm.edu.pl/ksiazki/fm/fm19/fm19115.pdf
- Levine, N., “Semi-open sets and semi-continuity in topological spaces”, The American mathematical monthly 1963; 70(1): 36-41. doi:10.2307/2312781
- Modak, S. and Noiri, T., “A weaker form of connectedness”, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 2016; 65(1): 49-52.
- Modak, S. and Islam, Md., “More connectedness in topological spaces”, Caspian Journal of Mathematical Sciences (CJMS) peer 2019; 8(1): 74-83. doi:10.22080/cjms.2018.13741.1333
- Munkres, J.R., “ Topology”, Pearson Education 2014.
- Neubrunnova, A., “On certain generalizations of the notion of continuity”, Matematick‘ycasopis 1973; 23(4): 374-380. doi:https://dml.cz/handle/10338.dmlcz/126571
- Neubrunn, T., “A generalized continuity and product spaces”, Mathematica Slovaca 1976; 26(2): 97-99. doi:https://dml.cz/handle/10338.dmlcz/136112
- Neubrunn, T., “Quasi-continuity”, Real Analysis Exchange 1988; 12(2): 259-306. doi:10.2307/44151947
- Noiri, T., “A function which preserves connected spaces”, asopis pro Pstovn Matematiky 1982; 107(4):393-396. doi:10.21136/CPM.1982.118148
- Noiri, T. and Modak, S., “Half b-connectedness in topological spaces”, Journal of the Chungcheong Mathematical Society 2016; 29(2): 221-221. doi:10.14403/jcms.2016.29.2.221
- Pipitone, V. and Russo, G., “Spazi semiconnessi e spazi semiaperti”, Rendiconti del Circolo Matematico di Palermo 1975; 23(4): 273-285. doi:10.1007/BF02843735
- Tyagi, B.K., Bhardwaj, M. and Singh, S., “αβ-Connectedness as a characterization of connectedness”, Journal of advanced studies in topology 2018; 9(2): 119-129. doi:10.20454/jast.2019.1497
- Tyagi, B.K., Singh, S., et.al., “Some strong forms of connectedness in topological spaces”, Journal of advanced studies in topology 2019; 10(1): 20-27. doi:10.20454/jast.2019.149
References
Abd EI-Monsef, M.E., Mahmoud, R.A., and El-Deeb, S.N., “β-open sets and β-continuous mappings”, Bull. Fac. Sci. Assiut Univ 1983; 12(1): 77-90.
Andrijevi, D., “On B-open Sets”, Matematiki Vesnik 1996; 48: 59-64. doi:http://eudml.org/doc/252912
Baire, R., “Sur les fonctions de variables reelles”, Annali di Matematica Pura ed Applicata 1899; 3(1):1-123. doi:10.1007/BF02419243
Ekici, E., “On separated sets and connected spaces”, Demonstratio Math 2007; 40(1): 209-217. doi:10.1515/dema-2007-0122
Jafari, S. and Noiri, T., “Properties of β-connected spaces”, Acta Mathematica Hungarica 2003; 101(3): 227-236. doi:10.1023/B:AMHU.0000003907.90823.79
Kempisty, S., “Sur les fonctions quasicontinues”, fundamenta Mathematicae 1932; 1: 184-197. doi:http://matwbn.icm.edu.pl/ksiazki/fm/fm19/fm19115.pdf
Levine, N., “Semi-open sets and semi-continuity in topological spaces”, The American mathematical monthly 1963; 70(1): 36-41. doi:10.2307/2312781
Modak, S. and Noiri, T., “A weaker form of connectedness”, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 2016; 65(1): 49-52.
Modak, S. and Islam, Md., “More connectedness in topological spaces”, Caspian Journal of Mathematical Sciences (CJMS) peer 2019; 8(1): 74-83. doi:10.22080/cjms.2018.13741.1333
Munkres, J.R., “ Topology”, Pearson Education 2014.
Neubrunnova, A., “On certain generalizations of the notion of continuity”, Matematick‘ycasopis 1973; 23(4): 374-380. doi:https://dml.cz/handle/10338.dmlcz/126571
Neubrunn, T., “A generalized continuity and product spaces”, Mathematica Slovaca 1976; 26(2): 97-99. doi:https://dml.cz/handle/10338.dmlcz/136112
Neubrunn, T., “Quasi-continuity”, Real Analysis Exchange 1988; 12(2): 259-306. doi:10.2307/44151947
Noiri, T., “A function which preserves connected spaces”, asopis pro Pstovn Matematiky 1982; 107(4):393-396. doi:10.21136/CPM.1982.118148
Noiri, T. and Modak, S., “Half b-connectedness in topological spaces”, Journal of the Chungcheong Mathematical Society 2016; 29(2): 221-221. doi:10.14403/jcms.2016.29.2.221
Pipitone, V. and Russo, G., “Spazi semiconnessi e spazi semiaperti”, Rendiconti del Circolo Matematico di Palermo 1975; 23(4): 273-285. doi:10.1007/BF02843735
Tyagi, B.K., Bhardwaj, M. and Singh, S., “αβ-Connectedness as a characterization of connectedness”, Journal of advanced studies in topology 2018; 9(2): 119-129. doi:10.20454/jast.2019.1497
Tyagi, B.K., Singh, S., et.al., “Some strong forms of connectedness in topological spaces”, Journal of advanced studies in topology 2019; 10(1): 20-27. doi:10.20454/jast.2019.149