Abelization of join spaces of affine transformations of ordered field with proximity
نویسنده
چکیده
Using groups of affine transformations of linearly ordered fields a certain construction of non-commutative join hypergroups is presented based on the criterion of reproducibility of semi-hypergroups which are determined by ordered semigroups. The aim of this paper is to construct the abelization of the non-commutative join space of affine transformations of ordered fields. A construction of commutative weakly associative hypergroup (Hν-group) is made and a proximity is defined on this structure. 2000 AMS Classification: 20F60, 20N20
منابع مشابه
State spaces of $K_0$ groups of some rings
Let $R$ be a ring with the Jacobson radical $J(R)$ and let $picolon Rto R/J(R)$ be the canonical map. Then $pi$ induces an order preserving group homomorphism $K_0picolon K_0(R)to K_0(R/J(R))$ and an affine continuous map $S(K_0pi)$ between the state space $St(R/J(R))$ and the state space $St(R).$ In this paper, we consider the natural affine map $S(K_0pi).$ We give a condition ...
متن کاملNon-Archimedean fuzzy metric spaces and Best proximity point theorems
In this paper, we introduce some new classes of proximal contraction mappings and establish best proximity point theorems for such kinds of mappings in a non-Archimedean fuzzy metric space. As consequences of these results, we deduce certain new best proximity and fixed point theorems in partially ordered non-Archimedean fuzzy metric spaces. Moreover, we present an example to illustrate the us...
متن کاملBest proximity point theorems in 1/2−modular metric spaces
In this paper, first we introduce the notion of $frac{1}{2}$-modular metric spaces and weak $(alpha,Theta)$-$omega$-contractions in this spaces and we establish some results of best proximity points. Finally, as consequences of these theorems, we derive best proximity point theorems in modular metric spaces endowed with a graph and in partially ordered metric spaces. We present an ex...
متن کاملVector Space semi-Cayley Graphs
The original aim of this paper is to construct a graph associated to a vector space. By inspiration of the classical definition for the Cayley graph related to a group we define Cayley graph of a vector space. The vector space Cayley graph ${rm Cay(mathcal{V},S)}$ is a graph with the vertex set the whole vectors of the vector space $mathcal{V}$ and two vectors $v_1,v_2$ join by an edge whenever...
متن کاملActions of Join Spaces of Continuous Functions on Hypergroups of Second-Order Linear Differential Operators
One from classical constructions of algebraic binary hyperstructures (semihypergroups and hypergroups) from ordered algebraic systems is based on a certain Lemma on principal ends generated by products of pairs of elements – shortly termed as Ends-Lemma. First version of this auxiliary lemma was obtained in the monography [3]. The mentioned lemma is applied not only in case of hyperstructures c...
متن کامل