θ ω−Connectedness and ω −R 1 properties
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 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.
| Main Authors: | , |
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| Format: | Digital revista |
| Language: | English |
| Published: |
Universidad Católica del Norte, Departamento de Matemáticas
2019
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| Online Access: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000500921 |
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