Rekha and indira 4, 6 introduced dc,bset, bopen set in topological spaces. Rekha and indira 4, 6 introduced dc,bset, b open set in topological spaces. The notion of pre generalized bclosed sets and its di. Introduction to topological spaces and setvalued maps. In this paper, we introduce and study a new type of generalized open sets in topological spaces namely, pre. Generalized closed sets in topological spaces in this section, we introduce the concept of. Topological spaces in this section, we introduce the concept of g closed sets in topological spaces and study some of its properties. R, pg student, nirmala college for women, coimbatore,tamil nadu. 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. Nalayini research centre, department of mathematics, govindammal aditanar college for women, tiruchendur628 215, tamil nadu, india. In this paper, a new class of generalized open sets in a topological space, called pre regular spopen sets, is introduced and studied.
On supra ba open sets and supra bcontinuity on mafiadoc. 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. Gnanambal 10 have introduce the concept of generalized pre regular closed sets in topological spaces. On pre open sets in topological spaces and its applications. Semiopen sets and pre open sets in tri topological space. Since ynais open, f 1yna is open and therefore f 1a xnf 1yna is closed.
Topology by replacing open sets with semi open sets. Bcopen subsets of a topological space is denoted by. 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 addition, we discuss some applications of generalized neutrosophic preclosed sets, namely neutrosophic p t 1 2 space.
On generalized closed sets and generalized preclosed sets. Noiri gave a new type of generalized closed sets in topological space called gp closed sets. In 1970 levine first introduced the concepts of generalized closed sets in topological spaces. Semiprecontinuous functions and properties of generalized. Bechalli and bansali 2 somewhat bcontinuous functions and somewhat b. Also, we would like to discuss the applications of topology in industries. The authors in 8 have studied properties of those finite spaces. In this paper, the concept of generalized neutrosophic preclosed sets and generalized neutrosophic preopen sets are introduced.
In 2011, sharmistha bhattacharya 9 have introduced the notation of. Pdf in 1993, raychaudhuri and mukherjee 10 in troduced the notions of preopen sets and preclosure. Soft semi open sets and its properties were introduced and studied by bin chen4. In this paper, we introduced and studies new class of sets called generalized pre regular weakly closed set brie. Chapter 9 the topology of metric spaces uci mathematics. Y between topological spaces is continuous if and only if the inverse image of every closed set is closed. This class is contained in the class of semipreclopen sets and cotains all preclopen sets. Pdf preopen sets and resolvable spaces semantic scholar. 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. Ais a family of sets in cindexed by some index set a,then a o c. 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. Generalized pre regular weakly closed sets 1985 proof.
Finite topological spaces became much more essential in topology,with the development of computer science and the need for digital topology. The main objective is to give an introduction to topological spaces and setvalued maps for those who are aspiring to work for their ph. Soft semiopen sets and its properties were introduced and studied by bin chen4. In this paper, a new class of generalized open sets in a topological space, called pre regular sp open sets, is introduced and studied. Generalizations of rough functions in topological spaces by. In this paper, we introduce a new class of open sets that is called isopen set. On generalized closed sets and generalized preclosed sets in. Bc open sets is not set in general as shown by the following example. On nano generalized pre regular closed sets in nano. We obtain decompositions of regular open sets by using preregular spopen sets. 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. Soft regular generalized bclosed sets in soft topological.
Maki et al 1 introduced the concepts of generalized pre closed sets and pre generalized closed sets in an analogous manner. In this paper, we will generalize the intuitionistic fuzzy semipre open sets and intuitionstic fuzzy semipre continuous mappings using the concept of gradation of openness in ifuzzy topological spaces and also investigate their characteristic properties. Pre closed set, pre open set, gp closed, gp open set. Pdf in this paper, the author introduce and study the notion of pre. In a topological space x, if x and are the only regular semi open sets, then every subset of x is irclosed set. Suppose a z, then x is the only the only regular semi open set containing a and so r cla x. 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. On generalized pre regular weakly gprwclosed sets in. The aim of this paper is to continue the study of pre generalized bclosed sets. 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. Generalized pre open sets in a topological space ijert. 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. It is assumed that measure theory and metric spaces are already known to the reader. 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.
Generalizations of rough functions in topological spaces by using pre open sets 129 ction defined by. In section 2, we will initiate the notion of rough real. Gentry and hoyle 3 introduced and studied the concept of somewhat continuous and somewhat open functions in topological spaces. Pdf on generalized closed sets and generalized pre. We call open sub msets of an mtopological space x, an mopen subset, and. On generalized pre open sets in a topological space. Soft regular generalized bclosed sets in soft topological spaces. Find necessary and sufficient conditions under which every preopen set is open. Preregular spopen sets in topological spaces cubo, a.
On preopen sets in topological spaces and its applications a. Following the same technique, ogata in 1991defined an operation. Contra bc continuous functions in topological spaces. Mashhour 5 introduced pre open sets in topological spaces. 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. Dontchevin 1999 introduced preiopen sets, kasaharain 1979 defined an operation. Somewhat bcontinuous and somewhat bopen functions in. 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. Let x be a topological space and x, be the regular semi open sets. 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.
Abstract in this paper we introduce a new class of sets namely, gsclosed sets, properties of this set are investigated and we. 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. Noiri shiokita cho, hinagu, yatsushiro shi, kuvempu university kumamoto ken, 8695142 japan. Informally, 3 and 4 say, respectively, that cis closed under. On preaopen sets and contra preacontinuous functions. The aim of this paper is to investigate the properties of these sets in the ideal topological spaces.
Find conditions under which the intersection of any two preopen sets preopen. Show that the subset mnfxgis open in the metric topology. Find, read and cite all the research you need on researchgate. Rajarubi abstract in this paper, we introduce a new class of sets called. Since every closed set in a topological space is preclosed therefore pcla. Now, we introduce new classes of topological spaces in terms of the concept of pre open sets. Semigeneralized pre closed sets in topological spaces.
Elatrash and mahdi in 9 have studied the properties of a more general class of spaces than finite spaces yet is a. Also, we present the notion of iscontinuous, isopen, isirresolute, istotally continuous, and iscontracontinuous mappings, and we investigate some properties of these mappings. 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. Ogata, operation on topological spaces and associated topology, math. This class is contained in the class of semipreclopen sets and cotains all pre clopen sets. Applications of pre open sets young bae jun, seong woo jeong, hyeon jeong lee and joon woo lee abstract. L, assistant professor, nirmala college for women, coimbatore, tamil nadu. Generalizations of rough functions in topological spaces.
Semipre open sets and semipre continuity in gradation of. In the beginning we will study rough sets on the real line. We also study relations and various properties between the other existing neutrosophic open and closed sets. Saisundara krishnan, a new class of semi open sets in a topological space, proc. Find conditions under which every denseinitself set is preopen.
X, form a topology on x which is finer than also, we show that pre. Semigenaralized pre closed sets we introduce the following definition. 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. Metricandtopologicalspaces university of cambridge. Rodgio and et al2 introduce d closed sets in topological spaces and studied their properties. Furthermore, we introduce some isseparation axioms, and ismappings are related with isseparation. The notion of preopen 19 set plays a significant role in general topology. 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.
Finite spaces are a subclass of the class of t0alexandroff spaces. Pdf in this paper, a new class of generalized open sets in a topological space, called preregular spopen sets, is introduced and studied. Semigeneralized pre closed sets in topological spaces international journal of scientific and innovative mathematical research ijsimr page 76 lemma 2. Elatrash and mahdi in 9 have studied the properties of a more general class of spaces than finite. Jafari 7 discussed some applications of bopen sets in topological spaces on 2007. Supra topological pre open sets and its continuous functions are defined by o. Bc open subsets of a topological space is denoted by.
Introduction when we consider properties of a reasonable function, probably the. Several examples are provided to illustrate the behaviour of new sets. Arbitrary union of bc open sets in a topological space is set. 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. Some applications of preopen sets in topological spaces. On preaopen sets and contra preacontinuous functions and. 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. A subset a of a topological space x is called a pre d set if there are two u.
1220 561 1132 1552 936 1282 627 391 1415 213 323 584 448 1052 346 491 1245 1423 742 575 85 1128 1122 1472 845 1020 683 1273 1385 252 1428 1102 853