On generalized pre open sets in a topological space. Also, we present the notion of iscontinuous, isopen, isirresolute, istotally continuous, and iscontracontinuous mappings, and we investigate some properties of these mappings. On generalized closed sets and generalized preclosed sets. Informally, 3 and 4 say, respectively, that cis closed under. Metricandtopologicalspaces university of cambridge.
In this paper, we will generalize the intuitionistic fuzzy semi pre open sets and in tuitionstic fuzzy semi pre continuous mappings using the concept of gradation of open ness in ifuzzy topological spaces and also investigate their characteristic properties. Semigeneralized pre closed sets in topological spaces. Finite topological spaces became much more essential in topology,with the development of computer science and the need for digital topology. Saisundara krishnan, a new class of semi open sets in a topological space, proc. Some applications of preopen sets in topological spaces. In this paper, it will be shown that in ideal topological spaces, a set which is both closed set and semipre dense set is a closed set.
Now, we introduce new classes of topological spaces in terms of the concept of pre open sets. Pdf in this paper, a new class of generalized open sets in a topological space, called pre regular sp open sets, is introduced and studied. Maki et al 1 introduced the concepts of generalized pre closed sets and pre generalized closed sets in an analogous manner. Jafari 7 discussed some applications of bopen sets in topological spaces on 2007. Furthermore, we show that the category of topological spaces in the topos of msets has arbitrary products. The main aim of this paper is to introduce two new types of open sets, namely tri semi open sets and tri pre open sets in tri topological spaces along with their several properties and characterization. This applies, for example, to the definitions of interior, closure, and frontier in pseudometric spaces, so these definitions can also be carried over verbatim to a topological space. In section 2, we will initiate the notion of rough real. Rodgio and et al2 introduce d closed sets in topological spaces and studied their properties. In this paper, we introduce a new class of open sets that is called isopen set.
X, form a topology on x which is finer than also, we show that pre. Soft regular generalized bclosed sets in soft topological. It is assumed that measure theory and metric spaces are already known to the reader. Suppose that fis continuous and let a y be a closed set. A subset a of a topological space x is called a pre d set if there are two u. In this paper, a new class of generalized open sets in a topological space, called pre regular sp open sets, is introduced and studied. Using the concept of preopen set, we introduce and study topological properties of prelimit points, prederived sets, preinterior and preclosure of a set, preinterior points, preborder, prefrontier and preexterior. In this paper, a new class of sets called theta generalized pre open set in a topological space introduced and some of their basic properties are investigated. Since every closed set in a topological space is preclosed therefore pcla. We obtain decompositions of regular open sets by using preregular spopen sets. The notion of preopen 19 set plays a significant role in general topology. Let x be a topological space and x, be the regular semi open sets. Applications of pre open sets young bae jun, seong woo jeong, hyeon jeong lee and joon woo lee abstract.
This class is contained in the class of semipreclopen sets and cotains all pre clopen sets. Generalized pre regular weakly closed sets 1985 proof. On preopen sets in topological spaces and its applications a. Using the concept of pre open set, we introduce and study topological properties of pre limit points, pre derived sets, pre interior and pre closure of a set, pre interior points, pre border, pre frontier and pre exterior. In this research paper we are introducing the concept of mclosed set and mt space,s discussed their properties, relation with other spaces and functions. Generalized pre open sets in a topological space ijert. Generalizations of rough functions in topological spaces. On generalized closed sets and generalized preclosed sets in. In this paper, a new class of sets called theta generalized preopen set in a topological space introduced and some of their basic properties are investigated. Ais a family of sets in cindexed by some index set a,then a o c. In the beginning we will study rough sets on the real line. The aim of this paper is to continue the study of pre generalized bclosed sets. Suppose a z, then x is the only the only regular semi open set containing a and so r cla x.
Introduction when we consider properties of a reasonable function, probably the. Show that the subset mnfxgis open in the metric topology. In 2011, sharmistha bhattacharya 9 have introduced the notation of. In 1970 levine first introduced the concepts of generalized closed sets in topological spaces. Pdf in this paper, the author introduce and study the notion of pre. Mashhour 5 introduced pre open sets in topological spaces. Extension research of generalized closedness was done in recent years as the notion of generalized semi open sets, semi generalized open sets, generalized open sets, semi open sets, pre open sets and d open sets, semi pre open sets were investigated.
Furthermore, we introduce some isseparation axioms, and ismappings are related with isseparation. Following the same technique, ogata in 1991defined an operation. Generalized closed sets in topological spaces in this section, we introduce the concept of. The notion of pre generalized bclosed sets and its di. Rajarubi abstract in this paper, we introduce a new class of sets called. Pdf on generalized closed sets and generalized pre. On nano generalized pre regular closed sets in nano. The authors in 8 have studied properties of those finite spaces. Generalizations of rough functions in topological spaces by. After him csaszar introduced and studied the notions of g open sets, g semi open sets g preopen sets, g open sets in generalized topological spaces. Semipre open sets and semipre continuity in gradation of. Extension research of generalized closedness was done in recent years as the notion of generalized semiopen sets, semi generalized open sets, generalized open sets, semiopen sets, preopen sets and d open sets, semi preopen sets were investigated.
Semigeneralized pre closed sets in topological spaces international journal of scientific and innovative mathematical research ijsimr page 76 lemma 2. Soft regular generalized bclosed sets in soft topological spaces. Generalizations of rough functions in topological spaces by using pre open sets 129 ction defined by. Gnanambal 10 have introduce the concept of generalized pre regular closed sets in topological spaces. In this paper, we introduced and studies new class of sets called generalized pre regular weakly closed set brie. The purpose of this paper is to provide the new characterizations of semipreopen and semipreclosed sets by defining the concepts of semiprecontinuous mappings, semipreopen mappings, semipreclosed mappings, semipreirresolute mappings, pre semipreopen mappings, and pre semipreclosed mappings and study their characterizations in topological. Find conditions under which every denseinitself set is preopen. Pdf in 1993, raychaudhuri and mukherjee 10 in troduced the notions of preopen sets and preclosure. Semiopen sets and pre open sets in tri topological space. Semigenaralized pre closed sets we introduce the following definition.
Finite spaces are a subclass of the class of t0alexandroff spaces. A topological space in mset or simply an mtopological space, is an mset xwith a topology on it such that its open subsets are sub msets of x. Since ynais open, f 1yna is open and therefore f 1a xnf 1yna is closed. Soft semi open sets and its properties were introduced and studied by bin chen4. On preaopen sets and contra preacontinuous functions and. Contra bc continuous functions in topological spaces. On preaopen sets and contra preacontinuous functions. Topological spaces in this section, we introduce the concept of g closed sets in topological spaces and study some of its properties. In this paper, we introduce and study a new type of generalized open sets in topological spaces namely, pre.
The concept of pre open set in topological spaces was introduced in 1982. The main objective is to give an introduction to topological spaces and setvalued maps for those who are aspiring to work for their ph. Abstract in this paper we introduce a new class of sets namely, gsclosed sets, properties of this set are investigated and we. Soft semiopen sets and its properties were introduced and studied by bin chen4. Supra topological pre open sets and its continuous functions are defined by o. In this paper, a new class of generalized open sets in a topological space, called pre regular spopen sets, is introduced and studied. As application to tri open sets, tri semi open sets and tri pre open set, the authors introduce tri continuous, tri semi continuous, and tri.
Applications of preopen sets young bae jun, seong woo jeong, hyeon jeong lee and joon woo lee abstract. This class is contained in the class of semipreclopen sets and cotains all preclopen sets. Find conditions under which the intersection of any two preopen sets preopen. Pre closed set, pre open set, gp closed, gp open set. In this paper, it will be shown that in ideal topological spaces, a set which is both closed set and semi pre dense set is a closed set.
Preregular spopen sets in topological spaces cubo, a. On generalized closed sets and generalized pre closed sets in neutrosophic topological spaces article pdf available december 2018 with 582 reads how we measure reads. Elatrash and mahdi in 9 have studied the properties of a more general class of spaces than finite spaces yet is a. Gentry and hoyle 3 introduced and studied the concept of somewhat continuous and somewhat open functions in topological spaces. Semiprecontinuous functions and properties of generalized. Introduction to topological spaces and setvalued maps.
We call open sub msets of an mtopological space x, an mopen subset, and. Noiri gave a new type of generalized closed sets in topological space called gp closed sets. Y between topological spaces is continuous if and only if the inverse image of every closed set is closed. Noiri shiokita cho, hinagu, yatsushiro shi, kuvempu university kumamoto ken, 8695142 japan. Bcopen subsets of a topological space is denoted by. On pre open sets in topological spaces and its applications. Bc open sets is not set in general as shown by the following example.
Pdf preopen sets and resolvable spaces semantic scholar. Ogata, operation on topological spaces and associated topology, math. Several examples are provided to illustrate the behaviour of new sets. L, assistant professor, nirmala college for women, coimbatore, tamil nadu.
R, pg student, nirmala college for women, coimbatore,tamil nadu. On generalized pre regular weakly gprwclosed sets in. Pdf in this paper, a new class of generalized open sets in a topological space, called preregular spopen sets, is introduced and studied. Find necessary and sufficient conditions under which every preopen set is open. Nalayini research centre, department of mathematics, govindammal aditanar college for women, tiruchendur628 215, tamil nadu, india. Find, read and cite all the research you need on researchgate. We also study relations and various properties between the other existing neutrosophic open and closed sets. Chapter 9 the topology of metric spaces uci mathematics. Elatrash and mahdi in 9 have studied the properties of a more general class of spaces than finite. In addition, we discuss some applications of generalized neutrosophic preclosed sets, namely neutrosophic p t 1 2 space. Rekha and indira 4, 6 introduced dc,bset, bopen set in topological spaces. Elatik department of mathematics, faculty of science, tanat university, tanta, egypt abstract in this paper, we consider the class of preopen sets in topological spaces and investigate some of their properties.
In a topological space x, if x and are the only regular semi open sets, then every subset of x is irclosed set. Bechalli and bansali 2 somewhat bcontinuous functions and somewhat b. Somewhat bcontinuous and somewhat bopen functions in. In this paper, the concept of generalized neutrosophic preclosed sets and generalized neutrosophic preopen sets are introduced. Also, we would like to discuss the applications of topology in industries. Rekha and indira 4, 6 introduced dc,bset, b open set in topological spaces. On supra ba open sets and supra bcontinuity on mafiadoc. Bc open subsets of a topological space is denoted by. Muhammad shabir and munazza naz introduced soft topological spaces and the notions of soft open sets, soft closed sets, soft closure, soft interior points, soft neighborhood of a point and soft separation axioms. Topology by replacing open sets with semi open sets.
1159 92 762 812 874 890 606 482 680 755 101 1253 850 926 267 1297 279 776 352 1466 1382 216 1645 1610 981 1503 691 438 1499 1634 895 457 975 362 856 349 654 627 1242