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