θ ω−Connectedness and ω −R 1 properties
DOI:
https://doi.org/10.22199/issn.0717-6279-2019-05-0059Keywords:
Generalized open sets, θ-closure, θω-closure, R₁Abstract
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 θ ω -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 θ ω -continuous image of a connected set is θ ω -connected. We define and investigate V -θ ω -connectedness as a strong form of V - θ-connectedness, and we show that the θ ω -connectedness and V -θ ω -connectedness are independent. We continue the study of R 1 as a known topological property by giving several results regarding it. We introduce ω-R 1 (I), ω-R 1 (II), ω-R 1 (III) and weakly ω-R 1 as four weaker forms of R 1 by utilizing ω-open sets, we give several relationships regarding them and we raise two open questions.References
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