Sum connectedness in proximity spaces




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


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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Author Biographies

Beenu Singh, University of Delhi

Department of Mathematics

Davinder Singh, University of Delhi

Department of Mathematics


G. Bezhanishvili, Zero-dimensional proximities and zero-dimensional compactifications, Topology Appl. 156 (2009), 1496-1504.

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.

S. G. Mrówka and W. J. Pervin, On uniform connectedness, Proc. Amer. Math. Soc. 15 (1964), 446-449.

S. Naimpally, Proximity Approach to Problems in Topology and Analysis, Oldenbourg Verlag, München, 2009.

S. Naimpally and B. D. Warrack, Proximity Spaces, Cambridge Univ. Press, 1970.

Y. M. Smirnov, On completeness of proximity spaces I, Amer. Math. Soc. Trans. 38 (1964), 37-73.

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.




How to Cite

B. Singh and D. Singh, “Sum connectedness in proximity spaces”, Appl. Gen. Topol., vol. 22, no. 2, pp. 345–354, Oct. 2021.