θω−Connectedness and ω−R1 properties

Keywords: Generalized open sets, θ-closure, θω-closure, R₁

Abstract

We use the theta omega closure operator to define theta omega connectedness as a property which is weaker than connectedness and stronger than θ-connectedness. We give several sufficient conditions for the equivalence between θω-connectedness and connectedness, and between θω-connectedness and θ-connectedness. We give two results regarding the union of θω-connected sets and also we show that the weakly θω-continuous image of a connected set is θω-connected. We define and investigate V -θω-connectedness as a strong form of V - θ-connectedness, and we show that the θω-connectedness and V -θω-connectedness are independent. We continue the study of R1 as a known topological property by giving several results regarding it. We introduce ω-R1 (I), ω-R1 (II), ω-R1 (III) and weakly ω-R1 as four weaker forms of R1 by utilizing ω-open sets, we give several relationships regarding them and we raise two open questions.

Author Biographies

Samer Al Ghour, Jordan University of Science and Technology.
Department of Mathematics and Statistics.
Salma El-Issa, Jordan University of Science and Technology.
Department of Mathematics and Statistics.

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Published
2019-12-15
How to Cite
[1]
S. Al Ghour and S. El-Issa, “θω−Connectedness and ω−R1 properties”, Proyecciones (Antofagasta, On line), vol. 38, no. 5, pp. 921-942, Dec. 2019.
Section
Artículos