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Tytuł artykułu

Pβ-connectedness in topological spaces

Wybrane pełne teksty z tego czasopisma
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A new property called Pβ-connectedness is introduced which is stronger than connectedness and equivalent to pre-connectedness. The properties of this notion are explored and its relationship with other forms of connectedness, for example hyperconnectedness etc. are discussed. Locally pre-indiscrete spaces are defined as the spaces in which pre-open sets are closed. In such spaces connectedness becomes equivalent to pre-connectedness and hence to Pβ-connectedness, and semi-connectedness becomes equivalent to Pβ-connectedness. The notion of locally Pβ-connected space is introduced. The behavior of Pβ-connectedness under several types of mappings is investigated. An intermediate value theorem is obtained.
Wydawca
Rocznik
Strony
299--308
Opis fizyczny
Bibliogr. 15 poz.
Twórcy
autor
  • Atma Ram Sanatan Dharma College, University of Delhi, New Delhi-110021, India
autor
  • Department of Mathematics, University of Delhi, New Delhi-110007, India
autor
  • Department of Mathematics, University of Delhi, New Delhi-110007, India
Bibliografia
  • [1] Pipitone V., Russo G., Spazi semi connessi e spazi semiaperli, Rend. Circ. mat. Palermo, 1975, 24, 273-285
  • [2] Popa V., Propoerties of H-almost continuous functions, Bull. Math. Soc. Sci. Math. R.S. Roumanie (NS), 1987, 31, 163-168
  • [3] Jafari S., Noiri T., Properties of β-connected space, Acta math. Hungar., 2003, 101, 227-236
  • [4] Aho T., Nieminen T., Spaces in which preopen subsets are semi-open, Ricerche Mat., 1994, 43, 45-59
  • [5] Popa V., Noiri T., Weakly β- function, An. Univ. Timisoara Ser. Mat. Inform., 1994, 32, 83-92
  • [6] Levine N., Semi-open sets and semi-continuity in topological spaces, Amer. Mat. Monthly, 1963, 70, 36-41
  • [7] Mashhour A. S., Abd El-Monsef M. E., El-Deeb S. N., On pre-continuous and week pre-continuous mappings, Proc. Math. Phys. Soc. Egypt., 1982, 53, 47-53
  • [8] Njástad O., On some classes of nearly open sets, Pacific J. Math., 1965, 15, 961-970
  • [9] Abd El-Monsef M. E., El-Deep S. N., Mahmoud R. A., β-open sets and β-continous mappings, Bull. Fac. Sci. Assiut Univ., 1983, 12, 77-90
  • [10] Steen L. A., Seebach J. A., Counterexamples in topology, Holt, Rinehart and Winston, Inc., New York, 1970
  • [11] Andrijevié D., b-open sets, Mat. Vesnik., 1996, 48, 59-64
  • [12] El-Deeb N., Hasanein I. A., Mashbour A. S., Noiri T., On p-regular spaces, Bull. Math. Soc. Sci. Math. R.S. Roumanie (NS), 1983, 27(75), 311-315
  • [13] Dontchev J., Survey on pre-open sets, The Proceedings of the Yatsushiro Topological Conference, 1998, 1-18
  • [14] Reilly I. L., Vamanamurthy M. K., On α-continuity in topological spaces, Acta Math. Hugar., 1985, 45, 27-32
  • [15] Mahmoud R. A., Abd El-Monsef M. E., β-irresolute and β-topological invariant, Proc. Pakistan Acad., 1990, 3, 285-296
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-ea708cad-0720-40b9-a92d-af96d65fb220
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