Sum connectedness in proximity spaces

[EN] The notion of sum $ \delta $-connected proximity space which contains the category of $ \delta $-connected and locally $ \delta $-connected space is defined. Several characterizations of it are substantiated. Weaker forms of sum $ \delta $-connectedness are also studied.Singh, B.; Singh, D. (2021). Sum connectedness in proximity spaces. Applied General Topology. 22(2):345-354. https://doi.org/10.4995/agt.2021.14809345354222G. Bezhanishvili, Zero-dimensional proximities and zero-dimensional compactifications, Topology Appl. 156 (2009), 1496-1504. https://doi.org/10.1016/j.topol.2008.12.036R. 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.19780820113S. G. Mrówka and W. J. Pervin, On uniform connectedness, Proc. Amer. Math. Soc. 15 (1964), 446-449. https://doi.org/10.2307/2034521S. Naimpally, Proximity Approach to Problems in Topology and Analysis, Oldenbourg Verlag, München, 2009. https://doi.org/10.1524/9783486598605S. Naimpally and B. D. Warrack, Proximity Spaces, Cambridge Univ. Press, 1970. https://doi.org/10.1017/CBO9780511569364Y. M. Smirnov, On completeness of proximity spaces I, Amer. Math. Soc. Trans. 38 (1964), 37-73. https://doi.org/10.1090/trans2/038/03Y. 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