Sum connectedness in proximity spaces

Beenu Singh

https://orcid.org/0000-0003-0196-7670

India

University of Delhi

Department of Mathematics

Davinder Singh

India

University of Delhi

Department of Mathematics

Submitted: 2020-12-16

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Accepted: 2021-03-18

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Published: 2021-10-01

DOI: https://doi.org/10.4995/agt.2021.14809
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Keywords:

sum δ-connected, δ-connected, δ-component, locally δ-connected

Supporting agencies:

This research was not funded

Abstract:

The notion of sum δ-connected proximity spaces which contain the category of δ-connected and locally δ-connected spaces is defined. Several characterizations of it are substantiated. Weaker forms of sum δ-connectedness are also studied.
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References:

G. Bezhanishvili, Zero-dimensional proximities and zero-dimensional compactifications, Topology Appl. 156 (2009), 1496-1504. https://doi.org/10.1016/j.topol.2008.12.036

R. Dimitrijević and Lj. Kočinac, On connectedness of proximity spaces, Matem. Vesnik 39 (1987), 27-35.

R. Dimitrijević and Lj. Kočinac, On treelike proximity spaces, Matem. Vesnik 39, no. 3 (1987), 257-261.

V. A. Efremovic, Infinitesimal spaces, Dokl. Akad. Nauk SSSR 76 (1951), 341-343 (in Russian).

V. A. Efremovic, The geometry of proximity I, Mat. Sb. 31 (1952), 189-200 (in Russian).

J. K. Kohli, A class of spaces containing all connected and all locally connected spaces, Math. Nachr. 82 (1978), 121-129. https://doi.org/10.1002/mana.19780820113

S. G. Mrówka and W. J. Pervin, On uniform connectedness, Proc. Amer. Math. Soc. 15 (1964), 446-449. https://doi.org/10.2307/2034521

S. Naimpally, Proximity Approach to Problems in Topology and Analysis, Oldenbourg Verlag, München, 2009. https://doi.org/10.1524/9783486598605

S. Naimpally and B. D. Warrack, Proximity Spaces, Cambridge Univ. Press, 1970. https://doi.org/10.1017/CBO9780511569364

Y. M. Smirnov, On completeness of proximity spaces I, Amer. Math. Soc. Trans. 38 (1964), 37-73. https://doi.org/10.1090/trans2/038/03

Y. M. Smirnov, On proximity spaces, Amer. Math. Soc. Trans. 38 (1964), 5-35.

S. Willard, General Topology, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1970.

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