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Quotient space (topology) (X)

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 Book Id: WPLBN0002097649 Subjects: Non-Fiction, Education, Smarandache Collections ► Abstract Excerpt Details...-associative ring we need two separate algebraic structures say a commutative ring with 1 (or a field) together with a loop or a groupoid or a vector space or a linear algebra. The two non-associative well-known algebras viz. Lie algebras and Jordan algebras are mainly built using a vector space over a field satisfying special identities called the Jacobi identity and Jord... Full Text Search Details...TENTS Preface 5 1. BASIC CONCEPTS 1.1 Basics of vector space and bilinear forms 7 1.2 Smarandache vector spaces 8 1.3 Basic defi... ...e ring with 1 (or a field) together with a loop or a groupoid or a vector space or a linear algebra. The two non-associative well-known algebras viz... ...bras viz. Lie algebras and Jordan algebras are mainly built using a vector space over a field satisfying special identities called the Jacobi identit... ...f R has no SNA-ideals then we say R is SNA-simple ring. We define SNA-quotient ring for a given ring R and an SNA-ideal I; R / I is a Quotient r... ... as in the case of rings. One is not in a position to say whether the SNA- quotient rings of a SNA-maximal ideal is simple? The answer to this questio... ...subrings and not relative to the whole ring R. So one may presume that the quotient ring may have SNA-ideals relative to some other SNA-subrings. ... ...e refer [51] . We do not approach or define Jordan algebras using Zaraski topology. We purely deal it as an algebraic structure or to be more precis... ... viz. Smarandache Homological algebra, Smarandache manifolds, Smarandache topology and Smarandache linear algebras. Finally the dictionary on Lie alg...
 Book Id: WPLBN0002097100 ► Abstract Description Details...dels. Thus to construct the neutrosophic graphs one needs some of the neutrosophic algebraic structures viz. neutrosophic fields, neutrosophic vector spaces and neutrosophic matrices. So we for the first time introduce and study these concepts. As our analysis in this book is application of neutrosophic algebraic structure we found it deem fit to first introduce and study ... Full Text Search Details... ALGEBRAIC STRUCTURES 1.1 Neutrosophic Fields 7 1.2 Neutrosophic Vector spaces 8 Chapter Two SOME BASIC RESULTS ON GRAPH THEORY AND THE... ...osophic algebraic structures viz. neutrosophic fields, neutrosophic vector spaces and neutrosophic matrices. So we for the first time introduce and... ...ew neutrosophic algebraic structures like neutrosophic fields, neutrosophic spaces and neutrosophic matrices and illustrate them with examples. For ... ...sophic subgroups. Now we proceed on to define the notion of neutrosophic quotient group. DEFINITION 1.2.3: Let G (I) = 〈G ∪ I 〉 be a neutrosop... ...‘+’, suppose P(I) be a neutrosophic subgroup of G (I) then the neutrosophic quotient group )} ( ) ( { ) ( ) ( I G a I P a I P I G ∈ + = . Exam... ...r addition, P =2Z(I ) is a neutrosophic subgroup of Z(I ), the neutrosophic quotient group )} ( ) ( 2 { ) ( I Z a I Z a P I Z ∈ + = = {(2n+1) + (... ...has acted as a catalyst in the branch of mathematics known as combinatorial topology and is closely related to the currently fashionable field of gr...
 Book Id: WPLBN0002097043 Subjects: Non Fiction, Algebra, Smarandache Collections ► Abstract Full Text Search Details...TURES AND S-BISTRUCTURES 2.1 Basic concepts of bigroups and bivector spaces 37 2.2 Introduction of S-bigroups and S-bivector spaces 46 ... ... 51 3.2 Linear bitransformation and linear bioperators 62 3.3 Bivector spaces over finite fields 93 3.4 Representation of finite bigroup 95 ... ...raphs 102 3.6 Jordan biform 108 3.7 Application of bivector spaces to bicodes 113 3.8 Best biapproximation and its application 123 ... ...sophic subgroups. Now we proceed on to define the notion of neutrosophic quotient group. DEFINITION 4.1.6: Let G (I) = 〈G ∪ I 〉 be a neutrosophi... ...’, suppose P (I) be a neutrosophic subgroup of G (I) then the neutrosophic quotient group () {( )( ) } () GI aPIaGI PI =+ ∈ . Example 4.1.8: L... ...ition P = 2Z(I) is 135 a neutrosophic subgroup of Z(I), the neutrosophic quotient group using subgroup 2Z(I) is; )} I ( Z a ) I ( Z 2 a { P )... ...nd Cayley. Euler (1707-1782) became the father of graph theory as well as topology when in 1936 he settled a famous unsolved problem in his day cal...
 Book Id: WPLBN0002097651 Subjects: Non-Fiction, Education, Smarandache Collections ► Abstract Full Text Search Details...zations 84 1.8 Fuzzy near-rings and their properties 94 1.9 Fuzzy vector spaces and fuzzy bivector spaces 119 1.10 Fuzzy semigroups and their prope... ... fuzzy rings: definitions and properties 291 4.2 Smarandache fuzzy vector spaces and its properties 303 4.3 Smarandache fuzzy non-associative rings ... ...e fuzzy semirings and its properties 333 5.2 Smarandache fuzzy semivector spaces 341 5.3 Smarandache fuzzy non-associative semirings 352 5.4 Smaran... ... for all x, y ∈ R. Now we proceed on to recall the definition of fuzzy quotient ideal of ring R. DEFINITION [109]: If µ is any fuzzy ideal of a... ...f R µ defined by µ ' (µ x ∗ ) = µ (x) for all x ∈ R is called the fuzzy quotient ideal determined by µ . The proof can be had from [109]. T... ...bring of an integral domain R to be extendable to a fuzzy subfield of the quotient field. To this end we just recall the definition of fuzzy quasi-l... ...on groups. For more about these refer [139]. DEFINITION 1.12.1: A fuzzy topology τ on a group G is called a g fuzzy topology. The pair (G, τ) is c... ...nd arbitrary union of members of τ is a member of τ. Hence τ is a g-fuzzy topology on G. DEFINITION 1.12.2: Let τ 1 and τ 2 be g-fuzzy topologie... ... THEOREM 1.12.1: Let G 1 and G 2 be any two groups. If τ 1 is a g-fuzzy topology on the group G 1 and τ 2 is an indiscrete g-fuzzy topology on t...
 Book Id: WPLBN0002097101 Subjects: Non Fiction, Education, Smarandache Collections ► Abstract Full Text Search Details...raphs, neutrosophic fields, neutrosophic matrices and neutrosophic vector spaces. We provide many illustrations and applications relating NCMs. In t... ...ion, Park and Kim [78] deal with time lags on not continuous but discrete space. The t ij is a value in a finite set Ω of M-many values Ω = M 1 t }... ...cal concepts that underlie the design of OP#1. These concepts are: E-mail Space, Text Classification, Plant Behavior Architecture, and Sculptural Pr... ...phic subgroups. Now we proceed on to define the notion of neutrosophic quotient group. DEFINITION 2.2.6: Let G (I) = 〈G ∪ I〉 be a neutrosophic ... ..., suppose P (I) be a neutrosophic subgroup of G (I) then the neutrosophic quotient group )} ( ) ( { ) ( ) ( I G a I P a I P I G ∈ + = . Exampl... ...phic subgroup of Z(I) the neutrosophic subgroup of Z(I), the neutrosophic quotient group )} I ( Z a ) I ( Z 2 a { P ) I ( Z ∈ + = = {(2n+1) + (2n... ...nd Cayley. Euler (1707-1782) became the father of graph theory as well as topology when in 1936 he settled a famous unsolved problem in his day calle...
 Book Id: WPLBN0002097095 ► Abstract Full Text Search Details...ﬁne a Klein surface. A Klein surface is a Hausdorﬀ, connected, topological space S together with a family = {(U i ,φ i ) |i ∈ I} such that the chart... ...olyai-Gauss and Riemannian geometries may be united altogether in the same space, by some Smarandache geometries. These last geometries can be either ... ...a subspace) and with the Parallel Universes (because they combine separate spaces into one space) too([32]). Chapter 1 Preliminary 3 In [61], Smarand... ...hat Γ is a non-euclidean crystallographic group( shortly NEC group) if the quotient H/Γ is compact. More results can be seen in [11]. Typical results ... ...ing to the Lemma 2.2.1, given a map M and a group G AutM, we can deﬁne a quotient map M/G = (X α,β /G,P/G) as follows. X α,β /G ={x G |x∈X α,β }, wh... ...(x G ) is labelled by a unique element in G. Now we assign voltages on the quotient map M/G = (X α,β /G,P/G). If βx = y,y ∈ π −1 (y G ) and the label ... ...o other branch mathematics, one typical example is its contribution to the topology for the classiﬁcation of compact surfaces by one face, or its dual... ....Appl.Math. & Com- puting, Vol.17(2005), 25-38. [52] W.S.Massey, Algebraic topology: an introduction, Springer-Verlag,New York, etc.(1977). [53] B.Moh... ....R.Stallings),Princeton University Press,1987. [64] J.Stillwell, Classical topology and combinatorial group theory, Springer-Verlag New York Inc., (19...
 Book Id: WPLBN0001235286 Subjects: Non Fiction, Philosophy, Science ► Abstract Full Text Search Details...of the behaviors of all complex systems on to a tiny sliver of the state (or phase) space (sort of a mega attractor basin). According to this view, ... ... of as attractors. Contexts can be thought of as attractor landscapes in the phase space of language. They can also be described as fitness landsca... ...he universe (theories) tend to be continuous. Newtonian time is equated to a river. Space is a yarn. Einstein was the last classicist (relativity ju... ...inapplicable philosophically and practically. There is a continuum of intelligence quotients (I.Q.s) and, yet, the gifted person is not an enhanced... ...black branes delineate a cosmological evolutionary tree - from a universe with one topology to another, with another topology. Our world may be the...
 Book Id: WPLBN0001235224 Subjects: Non Fiction, Education, Economics ► Abstract Full Text Search Details...hy not extend the woman's ownership of her body and right to it further in time and space to the post-natal period? Contracts to provide goods and ... ...use" has been raised with every scientific advance - from in vitro fertilization to space travel. Every technology can be potentially abused. Telev... ...s. - Through legislation, bureaucracy, control of the media, cornering advertising space in the media, controlling infrastructure, owning intellec... ...inapplicable philosophically and practically. There is a continuum of intelligence quotients (I.Q.s) and, yet, the gifted person is not an enhanced... ...black branes delineate a cosmological evolutionary tree - from a universe with one topology to another, with another topology. Our world may be the...
 Book Id: WPLBN0001235225 Subjects: Non Fiction, Religion, Philosophy ► Abstract Full Text Search Details...hy not extend the woman's ownership of her body and right to it further in time and space to the post-natal period? Contracts to provide goods and ... ...use" has been raised with every scientific advance - from in vitro fertilization to space travel. Every technology can be potentially abused. Telev... ...s. - Through legislation, bureaucracy, control of the media, cornering advertising space in the media, controlling infrastructure, owning intellec... ...inapplicable philosophically and practically. There is a continuum of intelligence quotients (I.Q.s) and, yet, the gifted person is not an enhanced... ...black branes delineate a cosmological evolutionary tree - from a universe with one topology to another, with another topology. Our world may be the...
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