International Journal of Modern Science and Technology Β· ISSN 2456-0235

Research Article Β· Mathematical Sciences Β· Volume 4, Issue 3 Β· Mar 2019 Β· Pages 75–78

Certain Open Sets in Hereditary Generalized Topological Spaces

B. Okelo

  • B. Okelo: School of Mathematics and Actuarial Science, Jaramogi Oginga Odinga University of Science and Technology, P. O. Box 210-40601, Bondo-Kenya.

Abstract

Characterization of sets in topological spaces has been carried out by many mathematicians over a period of time. However, characterizing hereditary topological spaces has not been exhausted. Certain aspects of these open sets include 𝜏-open sets, 𝜏-β„‹-open sets, and open functions among others. In this paper, we study in particular the concepts of 𝜏-open sets and 𝜏-β„‹-open sets. We also give some characterizations of 𝜏-β„‹- continuous and 𝜏-β„‹-open functions. Lastly, certain properties of 𝜏-β„‹-open sets are outlined.

Keywords

𝜏-open sets; 𝜏-β„‹-open sets; 𝜏-β„‹-open functions; 𝜏-continuous functions

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