The concept of gyrogroups is a generalization groups which do not explicitly have associativity. In this paper, the notion fuzzy gyronorms on introduced. relations metrics (in sense George and Veeramani), are studied. Also, metric structures normed discussed. Finally completion gyrogroup with an invariant We mainly show that if d G (Gˆ,dˆ) space (G,d); then for any continuous t-norm ⁎, standard...

Separability is one of the most basic and important topological properties. In this paper, separability in (strongly) gyrogroups studied. It proved that every first-countable left ?-narrow strongly gyrogroup separable. Furthermore, it shown if a feathered G isomorphic to subgyrogroup separable gyrogroup, then Therefore, metrizable separable, locally compact

Suppose that (T;*) is a groupoid with left identity such each element 2 T has inverse. Then called gyrogroup if and only (i) there exists function gyr : x -Aut(T) for all a; b; c T, * (b c) = (a b) ? gyr[a; b]c, where b]c gyr(a; b)(c); (ii) b b] gyr[a b]. In this paper, the structure of normal subgyrogroups certain gyrogroups are investigated.

Using Klein's approach, geometry can be studied in terms of a space points and group transformations that space. This allows us to apply algebraic tools studying mathematical structures. In this article, we follow approach study the $(G, \mathcal{T})$, where $G$ is an abstract gyrogroup $\mathcal{T}$ appropriate containing all gyroautomorphisms $G$. We focus on $n$-transitivity gyrogroups also ...

A space X is submaximal if any dense subset of open. In this paper, we prove that every topological gyrogroup non-measurable cardinality strongly ?-discrete. Moreover, hereditarily paracompact.

This autobiography presents the scientific living of Abraham Ungar and his role in Gyrogroups and Gyrovector spaces.‎