Ipseparation axioms in ideal bitopological ordered spaces ii. The aim of this paper is to introduce a new closure operator and an associated new topology in bitopological spaces. There are several hundred works indicated to the investigation of bitopological spaces. Some connections and interrelations between tiseparation axioms i1,2,3 for bitopological spaces are considered.
Then some basic notions, including the bisoft open sets, bisoft closedsets, bisoft. In this paper, we introduce a new type of closed sets in bitopological space x. New types of generalized closed sets in bitopological spaces. Problems of the theory of bitopological spaces springerlink. Pdf operations on bitopological spaces researchgate. Herewestudy versions ofseparability inbitopological spaces. On bitopological spaces marcus john saegrove iowa state university follow this and additional works at.
Bokalo, the tangency of topologies and tangential properties of topological spaces,tr. Weak open sets in ideal bitopological spaces ijert. In this paper we introduce and study the notion of pairwise weakly lindelof bitopological spaces and obtain some results. We introduce and discus recent type of fibrewise topological spaces, namely fibrewise bitopological spaces, also, we introduce the concepts of fibrewise closed bitopological spaces, fibrewise open bitopological spaces, fibrewise locally sliceable bitopological. Semiopen and semiclosed set in bitopological spaces. A new closure operator in bitopological spaces and associated separation axioms rajeswari, r. Soft bitopological spaces were introduced and studied, in 2014, by ittanagi as a soft counterpart of the notion of bitopological space. Na this leads one to consider the set of points sometimes. Levine defined the notions of semiopen sets and semicontinuity in topological spaces. We continue the study of bitopological separation axioms that was begun by kelly and obtain some results. In this present study, we discuss softgsrclosed sets in soft bitopological spaces and their properties.
We also define some new separation axioms and a comparative study is done. On soft gsrclosed sets in soft bitopological spaces. Bitopological spaces arise in a natural way by considering the topologies induced by sets of the form b fy i px,y and applications. Therefore, these spaces are generalization of the bitopological ordered spaces and bitopological spaces.
In this paper, we introduce and study the concepts of quasi bopen and quasi bclosed functions on bitopological spaces. Also introduce and investigate some new separation axioms called pairwise soft t0, pairwise soft t1. Salleh, a note on pairwise continuous mappings and bitopological spaces, eur. Part of themathematics commons this dissertation is brought to you for free and open access by the iowa state university capstones, theses and dissertations at iowa state university digital repository. Research paper mathematics iraq volume 6 issue 2, february 2017. Kelly4, first initiated the concept of bitopological spaces. In this paper, introduce and study the concept of soft bitopological spaces which are defined over an initial universe with a fixed set of parameters. Further, we also study the pairwise weakly lindelof subspaces and subsets, investigate some of their properties and show that a pairwise weakly lindelof property is not a hereditary property. Weak open sets in ideal bitopological spaces written by nirmala rebecca paul published on 20702 download full article with reference data and citations. Andrew moshier journal of logic and algebraic programming 76 2008 161174 163 the collection na of open neighbourhoods of a point a in a topological space xforms a completely prime. Generalized bclosed sets in ideal bitopological spaces. Regular generalized star closed sets in bitopological spaces 343 theorem 3. In particular, four different versions of the definition of the pairwise hausdorff separation axion are discussed.
Morphisms between bitopological spaces are required to be continuous with respect to each of the two topologies. A note on pairwise continuous mappings and bitopological. Download fulltext pdf on metacompactness in bitopological spaces article pdf available in international journal of pure and applied mathematics 1191. Ittangi 1 initiated the concept in soft bitopological space in 2014. In this paper we recount some initial concepts and results of the general theory of bitopological spaces, understood as pairs x. A note on some generalized closed sets in bitopological spaces associated to digraphs kannan, k. In this paper, we introduce generalized alpha generalized closed sets g.
Rajakumar, on feeblylocally open sets in bitopological spaces, international journal of advances in mathematics, volume 2018, number 1, pages 2630, 2018. But it is preserved under perfect mappings in bitopological settings. Bitopological and topological ordered kspaces ralph koppermana. Pdf generalized bclosed sets in ideal bitopological spaces. In this paper, a new concept of bisoft bitopological space is introduced. This paper gives a survey of and problems in the study of bitopological spaces.
No connection between the two topologies is assumed. Lawsonb a city college of cuny, usa b louisiana state university, usa received 16 january 2003. These functions, called probabilistic quasipseudometrics and fuzzy quasipseudometrics, are generalisations of classical quasipseudo metrics. Topological space topological structure usual topology bitopological space. The importance of this approach is that, the class of multiset bitopological spaces is wider and more general than the class of bitopological spaces. Regular generalized star closed sets in bitopological spaces. The concept of bitopological spaces was first introduced by kellys. International journal of pure and applied mathematics. Pdf special functions on bitopological spaces researchgate. However, there is not a systematic study of selection principles theoryinbitopological context. A bitopological space is a set x together with two topologies. In this book, generally speaking, some properties of bitopological spaces generated by certain nonsymmetric functions are studied. Certain properties of bitopological spaces springerlink.
They are mainly related to function spaces see 7,14,17,19,22. Theory, relations with generalized algebraic structures and applications, volume 199 1st edition. A note on almost baire bitopological spaces dochviri, i. On the other hand, there are very few papers which deal with bitopological spaces and selection principles. Kelly 5 introduced the concept of bitopological spaces in 1963. In 1991, sundaram introduced the concept of generalized closed sets in bitopological spaces. Functional analysis in asymmetric normed spaces download. They used the notion of iincreasing decreasing sets and introduced separation axioms i pt iordered spaces, i 0, 1, 2 in ideal bitopological ordered spaces. The notion has been studied extensively in recent years by many topologists. On the pairwise weakly lindelof bitopological spaces. In this paper, using bitopological semiopen sets, an asymmetric generalization of haworthmccoys wellknown theorem 4, theorem 3.
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