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