{"id":19989,"date":"2018-03-13T08:13:13","date_gmt":"2018-03-13T08:13:13","guid":{"rendered":"http:\/\/qu.edu.iq\/repository\/?p=19989"},"modified":"2018-03-13T08:13:13","modified_gmt":"2018-03-13T08:13:13","slug":"%d8%b1%d8%b3%d8%a7%d9%84%d8%a9-%d8%a7%d9%84%d9%85%d8%a7%d8%ac%d8%b3%d8%aa%d9%8a%d8%b1%d8%aa%d8%ad%d8%aa-%d8%b9%d9%86%d9%88%d8%a7%d9%86-on-generalization-of-wb-open-sets-in-topological-spaces-%d9%84","status":"publish","type":"post","link":"https:\/\/repository.qu.edu.iq\/?p=19989","title":{"rendered":"\u0631\u0633\u0627\u0644\u0629 \u0627\u0644\u0645\u0627\u062c\u0633\u062a\u064a\u0631 \u0644\u0644\u0637\u0627\u0644\u0628 \u0632\u064a\u0646 \u0627\u0644\u0639\u0627\u0628\u062f\u064a\u0646 \u0639\u0628\u0627\u0633 \u0646\u0627\u0635\u0631 \u062a\u062d\u062a \u0639\u0646\u0648\u0627\u0646 (on generalization of wb-open sets in Topological spaces )"},"content":{"rendered":"<p style=\"text-align: center\"><strong>ABSTRACT<\/strong><\/p>\n<p style=\"text-align: center\">The main aim of this work is to expand and study some types of topological spaces \u00a0by -open sets .<\/p>\n<p style=\"text-align: center\">In this work,we extend these concepts by using -open sets to new definitions for -connected space, -compact space,countably \u03c9b-compact, -cluser Point, -lindelof space,then we study the relations between the above mentioned with other concepts like \u00a0 &#8211; , &#8211; , -regular, -normal,During the work,some important and new concepts have been illustrated including nearly -compact,nearly -lindelof in addition studing the behavior of \u00a0these qualities under the in-fluence of certain types of functions we also dealt with the concepts of -closed, -open functions, -continuou<\/p>\n<p style=\"text-align: center\">the properties of these functions .<\/p>\n<p style=\"text-align: center\">the following are among our main results:<\/p>\n<p style=\"text-align: center\">1- Let <em>\u00a0<\/em>be a bijective function \u00a0.<\/p>\n<p style=\"text-align: center\">i-\u00a0 If f is b-open and X is -space then Y is -space.<\/p>\n<p style=\"text-align: center\">ii- If f is b-continuous and Y is -space then X is -space .<\/p>\n<p style=\"text-align: center\">2- The door space is &#8211; \u00a0\u00a0if and only if it is &#8211; .<\/p>\n<p style=\"text-align: center\">3- The door space is &#8211; \u00a0if and only if it is &#8211;<\/p>\n<p style=\"text-align: center\">4- Let X be topological space, then the following statements are.equivalent:<\/p>\n<p style=\"text-align: center\">i- X is -compact.<\/p>\n<p style=\"text-align: center\">ii- Every maximal filterbase -converges to some points of \u00a0X.<\/p>\n<p style=\"text-align: center\">iii- Every filterbase -accumulates at some points of .X.<\/p>\n<p style=\"text-align: center\">5- A topological space X is \u03c9b-compact if and only if each net in X, has \u00a0at least one \u03c9b-cluster point .<\/p>\n<p style=\"text-align: center\">6- Let <em>\u00a0<\/em>be an.almost contra-\u03c9b-continuous, onto the following \u00a0statement<\/p>\n<p style=\"text-align: center\">\u00a0are equivalent<\/p>\n<p style=\"text-align: center\">i- if X is \u03c9b-compact, then Y is S-closed.<\/p>\n<p style=\"text-align: center\">ii- if X is \u03c9b-compact, then Y is S-Lindelof \u00a0.<\/p>\n<p style=\"text-align: center\">iii- if X is countably \u03c9b-compact,thenY is countably S-closed.<\/p>\n<p style=\"text-align: center\">\n","protected":false},"excerpt":{"rendered":"<p>ABSTRACT The main aim of this work is to expand and study some types of topological spaces \u00a0by -open sets &#8230; <a class=\"cz_readmore\" href=\"https:\/\/repository.qu.edu.iq\/?p=19989\"><i class=\"fa fa-sign-out\" aria-hidden=\"true\"><\/i><span>\u0642\u0631\u0627\u0621\u0629 \u0627\u0644\u0645\u0632\u064a\u062f<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[78],"tags":[],"class_list":["post-19989","post","type-post","status-publish","format-standard","hentry","category-78"],"_links":{"self":[{"href":"https:\/\/repository.qu.edu.iq\/index.php?rest_route=\/wp\/v2\/posts\/19989","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/repository.qu.edu.iq\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/repository.qu.edu.iq\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/repository.qu.edu.iq\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/repository.qu.edu.iq\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=19989"}],"version-history":[{"count":0,"href":"https:\/\/repository.qu.edu.iq\/index.php?rest_route=\/wp\/v2\/posts\/19989\/revisions"}],"wp:attachment":[{"href":"https:\/\/repository.qu.edu.iq\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=19989"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/repository.qu.edu.iq\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=19989"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/repository.qu.edu.iq\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=19989"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}