International journal of science and engineering research. We study the compactifcation of t0spaces generated by families of special continuous mappings into a given standard space e. Annals of the university of craiova mathematics and computer science series, 391, 2012. Let x,p1,p2 be a bitopological space then a subset a of x is say to be a semiopen set if a cl pi int pi a and semiclosed if int pi cl pi a a for i1or2. L mary tency 2 assistant professor in mathematics, nirmala college for women autonomous, department of mathematics, ppg institute of technology, coimbatore, india. Shabir and naz 26 defined the theory of soft topological space over an initial universe with a fixed set of parameters. The book 1 is a versatile introduction to the theory of bitopological spaces and its applications. Extra space between characters when converting justified word. Oct 29, 2018 the strong breed by wole soyinka pdf 9 nov the famous play written by wole soyinka, the strong breed tells the story of emen, who lives in a strange village and has to sacrifice his life. I am interested where bitopological spaces occur in various parts of mathematics i. If xr is a fuzzy point or a fuzzy singletone, then nxr. Function spaces and product topologies 243 let zegw. On feebly closed mappings in bitopological spaces zahir dobeas alnafie dept.
This search discusses the set and feebly closed sets in bitopological space, and these concepts define the feeblyclosed function, semiclosed function and pre. International journal of multidisciplinary research and. To a large extent, our presentation is influenced by the situation in bitopological spaces cf. On closed sets in bitopological spaces, malaya journal of matematics, vol. Bitopological spaces pdf in this paper, we introduce a new type of closed sets in bitopological space x. Phd continuity on bitopological spaces master homology groups and simplicial complex professional record. A study on i,j gs closed sets in bitopological spaces l. Bitopological spaces arise in a natural way by considering the topologies induced by sets of the form b fy i px,y college of education,babylon university 2007 abstract in this paper we define semiopen set and semiclosed set in bitoplogical space due to ratnesh kumar saraf,2000 which is used to define generalized continuous function. We have 1 genuine space but lots of gaps between characters and some of those are actually spaces.
A bitopological space x, t, t is a non empty set x equipped with two topologies t and t. A study of soft bitopological spaces is a generalization of the study of soft topological spaces as every soft bitopological space x. Faculty full name arwa mohammed abd alrahman alshibani. On preconnected sets in bitopological spaces alaa erees. Semiopen and semiclosed set in bitopological spaces yiezi.
Semi connectedness in bitopological spaces, journal of alqadisiyah for computer science and mathematics, alqadisiyah university, a special issue researches of the fourth international scientific conference second part, p. Gender in translation sherry simon complexity theory and the social sciences david byrne the general crisis of the seventeenth century science and social science malcolm williams principles of research design in the social sciences frank bechhofer the turn to biographical methods in social science prue chamberlayne. Community service board member, kilili secondary school 2012present. The purpose of this paper is to suggest the fuzzy ideals in fuzzy bitopological space. The introduction gives an idea of the origins of the basic notions, contents, methods, and problems both of the classical in the spirit of kelly and of the general theory of bitopological spaces. In addition to generalize the concept of fuzzy lclosed sets, fuzzy lcontinuity and lopen functions due to abd elmonsef et al1. Valeriu popa department of mathematics and informatics list of papers general topology 1973 1.
On the application of operator and group theoretic concepts in signal processing and cryptography, february 2019. In 2014 mandira kar and thakur 12 have been studied the notion of connectedness in ideal bitopological spaces, but the studying of such spaces by using the supratopological space has not been considered. It has a student population around 420 and a team of 16 energetic and dedicated faculty. Khalagai, the numerical range of some operators on. Pairwise concepts in bitopological spaces journal of the australian. Translated fromzapiski nauchnykh seminarov pomi, vol. Theory, relations with generalized algebraic structures and applications. I continuous functions in ideal bitopological spaces. This search discusses the set and feebly closed sets in bitopological space, and. An approximate solution of some differential equations with new type of interpolation. In 1961 kelly introduced the concept of bitopological spaces as an extension of topological spaces. The integrated ac97 sound controller gained support for up to six channel sound. By a standard argument on compact sets 8 theorem 5.
Not exhausting the entire subject, it reflects basic ideas and methods of the theory. Fuzzy ideals, fuzzy bitopological spaces, fuzzy lopen sets. Differential geometry and symmetric spaces invitation to the mathematics of fermatwiles yves hellegouarch geometry and its applications walter a. After the work of levine various authors 1,2, 4 have contributed. Alshibani rgcompact spaces and rgconnected spaces mathematica pannoneca, hengery2006 3 a. Concepts of fuzzy ideals and fuzzy local function were introduced by sarkar 5. Popa, asupra aplicatiilor monotone intre spatiile bitopologice on monotone functions between bitopological spaces, stud. Semiopen and semiclosed set in bitopological spaces by yiezi kadham mahdi department of mathematics, college of education,babylon university 2007 abstract in this paper we define semiopen set and semiclosed set in bitoplogical space due to ratnesh kumar saraf,2000 which is used to define generalized continuous function. We also study strongly zerodimensional ordered topological spaces and their relation with functorial quasiuniformities. The strong breed by wole soyinka pdf 9 nov the famous play written by wole soyinka, the strong breed tells the story of emen, who lives. I would also like to know where bitopological spaces have some applications in various parts in mathematics.
Sometimes there may be spaces but this is more often what you might see in the pdf text. Extra space between characters when converting justified word document to pdf. Properties of function spaces defined on sets of continuous functions on bitopological spaces. In this and a subsequent paper, we use the notion of iincreasing decreasing sets which based on the ideal i, to introduce separation axioms in ideal bitopological ordered spaces. Pdf special functions on bitopological spaces researchgate. Generalization of open sets in bitopological spaces. Bitopological strong separation axioms in this section, we introduce the notions of strong separation axioms in bitopological spaces.
The list of papers published by faculty this year is. A study on gb closed sets in topological bitopological and. Ipseparation axioms in ideal bitopological ordered spaces i. Department of mathematics is marching forward towards higher goals and accomplishments. Pdf the main purpose of this paper is to introduce and study the notion of multiset bitopological spaces. We also generalize the notion of fuzzy lopen sets due to abd elmonsef et al1. Corresponding to wellknown properties of topological spaces, there are versions for bitopological spaces. In the study of topological spaces many concepts of topology have been generalized by.
Weak open sets in ideal bitopological spaces, international journal of engineer ing research and technology, vol 2. However, when the two topologies in a bitopological space coincide, these notions reduce to equivalent conventional concepts of topological spaces. Valeriu popa department of mathematics and informatics. In this paper we define pairwise dmetacompac spaces and study their properties and there relations with other topological spaces. One of the situations where bitopological spaces occur naturally are asymmetric metric spaces or quasimetric spaces.
Pdf the primary purpose of this paper is to introduce and study two new types of functions on bitopological spaces called, i,jquasi bopen and. Pokhariyal, separation axioms on functional spaces defined on bitopological spaces, journal of advanced studies in topology, vol. Abstract the aim of this paper is to introduce and study some new fuzzy pairwise notion in fuzzy bitopological ideals spaces. The notion of ideal in topological spaces was studied by kuratowski 5 and vaidyanathaswamy 10. Republic of iraq ministry of higher education and scientific. The notion of connectedness in bitopological spaces has been studied by pervin 14, reily 15 and swart 16. In 2014 mandira kar and thakur 12 have been studied the notion of connectedness in ideal bitopological spaces, but the studying of such spaces by using. Mccallion between the theory of bitopological spaces and that of ordered topological spaces, we construct the dimension theory for ordered. A uniform approach to normality for topological spaces. Click sync in the bottom of the screen once you added your ebook and click done after the synchronization is complete. The paper is, in essence, a monograph devoted to the theory of bitopological spaces and its applications. A subset a of a bitopological space x, t, t is turned i, j semiopen if there exists a t. Extra space between characters when converting justified.
The theory of bit0d010gica1 spaces was first developed by kelly in 1963 21. This paper is the third part of a survey of recent results in the theory of bitopological spaces. Asian journal of mathematics and statistics, 61, 33 42, 20. Let x be a non empty set, a nonempty collection of subsets of x is said to form a topology on x if. Prebounded, totally prebounded and precompact sets. Phd internal examiner for mr loyford njagi, title of thesis. Kuratowski 7 and vaidyanathasamy 9 introduced and investigated the concept of ide als in topological spaces. Beginning with the most recent job rank place and address of work date associate professor mathematic departmentcollege of sciencedammam 1572008.
A bitopological space, is pairwise compact if each cover. It is shown that linear functional on topological vector spaces are smarandachely precontinuous. Bitopological spaces arise in a natural way by considering the topologies induced by sets of the form b fy i px,y spaces, which are generalizations of quasimetric spaces, also induce bitopological spaces. Let x 1 2 be a bitopological space and aa subset of x.
Many pdf files do not actually contain any text spaces. When i convert a justified word document to pdf, additional space appears between characters not just between words causing words to be fragmented so, the word determined will look like d eterm ined. A bitopological space x is said to satisfy the pairwise in. In this context we have introduced the notions of ethin and erough gcompacti. Pdf drm free there should be no additional application or software required. The main purpose of this paper is to introduce pairwise generalized bro spaces in bitopological spaces with the help of generalized bopen sets in bitopological spaces and give several. The department of mathematics was established in the year 1951. On rgcompact spaces international journal of engineering science and innovative technology ijesit, india2015 2 a. Semiopen and semiclosed set in bitopological spaces. Fuzzy ideals, fuzzy bitopological spaces, fuzzy lopen. Curriculum vitae imam abdulrahman bin faisal university. There are several hundred works indicated to the investigation of bitopological spaces.
Iv currently i am supervising the following student who has submitted his thesis 1. Learning mathematical thinking and writing randall maddox advanced engineering mathematics alan jeffrey discrete mathematics with applications. Several examples are discussed and many will known theorems are generalized concerning metacompac spaces. Introduction and preliminaries levine 3 introduced the concept of generalized closed sets in topological spaces. Halpin 1974 and birsan 1974, and uses the commutative diagrams which occur in schauerte 1988 and brummer 1977, 1982. They contain gaps between letters and the software has to guess if there is a space in the text. International journal of multidisciplinary research and modern education ijmrme issn online. In 2014 mandira kar and thakur 12 have been studied the notion of connectedness in ideal bitopological spaces. Io datsheet hub ich is a family of intel southbridge microchips used to manage data communications between a cpu and a motherboard. In this note an attempt has been made to see how much bitopological these pairwise. Alshibani irresolute mappings in bitopological spaces journal of inst. Jan 14, 2019 bitopological spaces pdf in this paper, we introduce a new type of closed sets in bitopological space x. Dec 16, 2010 many pdf files do not actually contain any text spaces. They are defined as metric spaces, but the symmetry in the definition of metric is omitted.
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