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On #RG-Compact spaces | ||
| journal of the college of basic education | ||
| Article 1, Volume 22, Issue 96, 2016, Pages 85-88 | ||
| Authors | ||
| ; College of Education; Dr. Salim Dawood Mohisn AL-Mustansiriya University; Department of Mathematics Muntaha Khudair Abbas Technical College of Management | ||
| Abstract | ||
| On #RG-Compact spaces Dr. Salim Dawood Mohisn AL-Mustansiriya University/ College of Education/ Department of Mathematics Muntaha Khudair Abbas Technical College of Management/Baghdad Middle Technical University Abstract: In this paper, we give a new type of compact spaces, and study some of their properties, namely #RG- compact space in topological spaces upon via the # rg-open set with modify some theorem of compact spaces. Keywords rg- open sets , rw-closed sets , # rg-open set and # rg-compact spaces 1- Introduction: In 1906, Freched used for the first time the term of compactness in topological space . Asha Mathur [1] described compactness and weaker forms through a table containing 72 properties . M.E.Abd EL- Monsef and Kozae [3] introduced a property P_(〖αβ〗_ᴽ )for generalized 1920 types of compactness and closeness. M.E.Abd EL-Monsef , A.E.Radwan , F.A.Ibrahem andA.I.Nasir [4] used the property P_(〖αβ〗_ᴽ )to generalized 15456 types of compactness and closeness .While, the concepts (#rg- closed sets , #rg-open sets, #RG- continuous functions and #RG- irresolute functions)were discussed and introduced by (S.A. Fathima and Mariasingam ,2012 , in [6 ],[7 ] ) . In this paper , we introduced a new type of compactness on topological spaces , namely #RG- compact , and we study some of their properties . Throughout this paper (X,) and (Y,) (or simply X and Y) represent topological spaces and the family of all #rg-open ( resp .#rg-closed) sets of a space (X,τ) denoted by # RGO(X,τ) ( resp . # RGC(X,τ) ) . For a subset A of a space X. cl(A), int (A) and Ac denoted the closure of A, the interior of A and the complement of A in X respectively. | ||
| Keywords | ||
| Open sets; closed sets; open set and; compact spaces | ||
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