International Journal of Modern Science and Technology

INDEXED IN 

​​​​​​​March 2019, Vol. 4, No. 3, pp 75-78. 

​​​Certain Open Sets in Hereditary Generalized Topological Spaces

B. Okelo*
School of Mathematics and Actuarial Science, Jaramogi Oginga Odinga University of Science and Technology,

P. O. Box 210-40601, Bondo-Kenya.

​​​*Corresponding author’s e-mail: bnyaare@yahoo.com

​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: πœ-open sets; 𝜏-β„‹-open sets; 𝜏-β„‹-open functions; 𝜏-continuous functions.

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ISSN 2456-0235