Proximity spaces via hereditary classes

Subject Areas : General topology

Gh.  Mirhosseinkhani ¹ (Department of Mathematics and Computer Sciences, Sirjan University of Technology, Sirjan, Iran)

Received: 2022-11-18 Accepted : 2022-12-16 Published : 2022-12-01

Keywords:

References:

[1] G. Beer, S. Levi, Total boundedness and bornologies, Topology Appl. 156 (7) (2009), 1271-1288.

[2] Á. Császár, Generalized topology, generalized continuity, Acta Math. Hungar. 96 (2002), 351-357.

[3] Á. Császár, Modification of generalized topologies via hereditary classes, Acta Math. Hungar. 115 (1-2) (2007), 29-36.

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

[5] P. Grzegrzolka, J. Siegert, Coarse proximity and proximity at infinity, Topology Appl. 251 (2019), 18-46.

[6] E. Hayashi, A note on proximity spaces, Bull. Aichi Gakngei Univ. 14 (1965), 1-4.

[7] E. Hayashi, On some properties of a proximity, J. math. Soc. Japan. 16 (1964), 375-378.

[8] H. Hogbe-Nlend, Bornologies and functional analysis, North-Holland, Amsterdam, 1977.

[9] D. Jankovic, T. R. Hamlet, New topologies from old via ideals, Amer. Math. Monthly. 97 (1990), 295-310.

[10] A. Kandila, O. A. Tantawyb, S. A. El-Sheikhc, A. Zakariac, I-proximity spaces, Jokull J. 63 (5) (2013), 237-245.

[11] S. Leader, Local proximity spaces, Math. Annalen. 169 (1967), 275-281.

[12] M. N. Mukherjee, D. Mandal, D. Dey, Proximity structure on generalized topological spaces, Afr. Mat. 30 (2019), 91-100.

[13] S. A. Naimpally, B.D. Warrack, Proximity Spaces, Cambridge University Press, 1970.

[14] W. J. Pervin, Quasi-proximities for topological spaces, Math. Annalen. 150 (1963), 325-326.

[15] F. Riesz, Stetigkeitsbegriff und abstrakte mengenlehre, Atti IV Congr. Intern. Mat. Roma. (1908), 18-24.