Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지
DOI QR코드

DOI QR Code

CONNECTEDNESS IN IDEAL PROXIMITY SPACES

  • Singh, Beenu (Department of Mathematics, University of Delhi) ;
  • Singh, Davinder (Department of Mathematics, Sri Aurobindo College, University of Delhi)
  • Received : 2020.10.28
  • Accepted : 2021.01.05
  • Published : 2021.03.25
Download PDF
⟨ Previous Next ⟩

Abstract

Two new concepts, namely, ��∗-connectedness and ��∗-component are introduced by using ideal in proximity spaces. A relation of ��∗-connectedness with different types of connectedness that are considered in literature before is studied. It is shown that ��∗-connectedness is a contractive property.

Keywords

References

  1. R. Dimitrijevic and Lj. Kocinac, On Connectedness of Proximity Spaces, Mat. Vesnik 39 (1) (1987), 27 - 35.
  2. Erdal Ekici and Takashi Noiri, Connectedness in Ideal Topological Spaces, Novi Sad J. Math. 38 (2) (2008), 65 - 70.
  3. Erdal Ekici and Takashi Noiri, *-hyperconnected ideal topological spaces, Analele Stiintifice Ale Universitatii Al. I. Cuza Din Iasi (S.N.) Matematica Tomul LV III, (2012), f. 1, 121 - 129.
  4. R.A. Hosny and O.A.E. Tantawy, New Proximities from old via Ideals, Acta Math. Hungar. 110 (1-2) (2006), 37 - 50. https://doi.org/10.1007/s10474-006-0005-0
  5. D. Jankovic and T. R. Hamlett, New Topologies from old via Ideals, Amer. Math. Monthly 97 1990, 295 - 310. https://doi.org/10.1080/00029890.1990.11995593
  6. K. Kuratowski, Topology Vol.1, New York Academic Press, 1966.
  7. S. Modak and T. Noiri, Connectedness of Ideal Topological Spaces, Filomat 29 (4) 2015, 661 - 665. https://doi.org/10.2298/FIL1504661M
  8. S. G. Mrowka and W. J. Pervin, On Uniform Connectedness, Proc. Amer. Math. Soc. 15 (1964), 446 - 449. https://doi.org/10.1090/S0002-9939-1964-0161307-7
  9. S. Naimpally, Proximity Approach to Problems in Topology and Analysis, Oldenbourg Verlag, Munchen, 2009.
  10. S. Naimpally, B.D. Warrack, Proximity Spaces, Cambridge Univ. Press, 1970.
  11. R. Vaidyanathaswamy, The localisation theory in set topology, Proc. Indian Acad. Sci. 20 (1944), 51 - 61. https://doi.org/10.1007/BF03048958