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...
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| Lenguaje: | English |
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Universidad Católica del Norte, Departamento de Matemáticas
2019
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oai:scielo:S0716-091720190005009212020-01-07θ ω−Connectedness and ω −R 1 propertiesAl Ghour,SamerEl-Issa,Salma 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 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.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.38 n.5 20192019-12-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000500921en10.22199/issn.0717-6279-2019-05-0059 |
| institution |
Scielo Chile |
| collection |
Scielo Chile |
| language |
English |
| topic |
Generalized open sets θ-closure θω-closure R₁ |
| spellingShingle |
Generalized open sets θ-closure θω-closure R₁ Al Ghour,Samer El-Issa,Salma θ ω−Connectedness and ω −R 1 properties |
| description |
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. |
| author |
Al Ghour,Samer El-Issa,Salma |
| author_facet |
Al Ghour,Samer El-Issa,Salma |
| author_sort |
Al Ghour,Samer |
| title |
θ ω−Connectedness and ω −R 1 properties |
| title_short |
θ ω−Connectedness and ω −R 1 properties |
| title_full |
θ ω−Connectedness and ω −R 1 properties |
| title_fullStr |
θ ω−Connectedness and ω −R 1 properties |
| title_full_unstemmed |
θ ω−Connectedness and ω −R 1 properties |
| title_sort |
θ ω−connectedness and ω −r 1 properties |
| publisher |
Universidad Católica del Norte, Departamento de Matemáticas |
| publishDate |
2019 |
| url |
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000500921 |
| work_keys_str_mv |
AT alghoursamer 9529698722connectednessand9698722r1properties AT elissasalma 9529698722connectednessand9698722r1properties |
| _version_ |
1718439859178176512 |