THERMAL SCIENCE

International Scientific Journal

Kadirhan Polat

ON SEPARATION AXIOMS ON LEFT AND RIGHT OPERAND TOPOLOGIES

ABSTRACT
In this paper, we examine separation axioms on left operand and right operand topologies generated by a raw binary operation which is weaker than the concepts of both partial and multivalued binary operation, and obtain some useful results.
KEYWORDS
raw binary operation, left topology, right topology, separation axiom
PAPER SUBMITTED: 2022-08-12
PAPER REVISED: 2022-09-10
PAPER ACCEPTED: 2022-09-25
PUBLISHED ONLINE: 2023-01-29
DOI REFERENCE: https://doi.org/10.2298/TSCI22S2621P
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2022, VOLUME 26, ISSUE Special Issue 2, PAGES [621 - 629]
REFERENCES
[1] Bruck, R. H., A Survey of Binary Systems, Springer Berlin, Heidelberg, Germany, 1971
[2] Clifford, A. H., Preston, G. B., The Algebraic Theory of Semigroups, American Mathematical Soc., Providence, Providence, R. J., USA, 1967, 10.1090/surv/007.2
[3] Gratzer, G., Universal Algebra, Springer, New York, USA, 2008
[4] Polat, K., Cagman, A., Polcag spaces: I. Group-Like Structures, Thai Journal of Mathematics, 19 (2019), 1, pp. 87-92
[5] Burris, S., Sankappanavar, H. P., A Course in Universal Algebra, Springer-Verlag, New York, USA, 1981, 10.1007/978-1-4613-8130-3
[6] Smithson, R. E., Topologies Generated by Relations, Bulletin of the Australian Mathematical Society, 1 (1969), 3, pp. 297-306, 10.1017/s0004972700042167
[7] Allam, A. A. et. al., Some Methods for Generating Topologies by Relations, Bulletin of the Malaysian Mathematical Sciences Society, 311 (2008), 1, pp. 35-45
[8] Indurain, E., Knoblauch, V., On Topological Spaces Whose Topology is Induced by a Binary Relation, Quaestiones Mathematicae, 36 (2013), 1, pp. 47-65, 10.2989/16073606.2013.780335
[9] Polat, K., Topologies Generated by Raw Binary Structures, Transactions in Mathematical and Computational Sciences, 1 (2021), 2, pp. 23-30, 10.52587/tmcs010203
[10] Lynn, A. S., Seebach, J. A., Counterexamples in Topology, Springer, New York, USA, 1978
[11] Merrifield, R. E., Simmons, H. E., Topological Methods in Chemistry, Wiley-Interscience, New York, USA, 1989
[12] Munkres, J., Topology, Pearson Education Limited, Harlow, UK, 2013
[13] Schechter, E., Handbook of Analysis and its Foundations, Academic Press, Cambridge, Mass., USA, 1996
[14] Willard S., General Topology, New York, USA, 2004
PDF VERSION [DOWNLOAD]
On separation axioms on left and right operand topologies

© 2026 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence