Geodesic loops.
Idempotents of compact monothetic semiclosure semigroups
Irresolvable countable spaces of weight less than
We construct in Bell-Kunen’s model: (a) a group maximal topology on a countable infinite Boolean group of weight and (b) a countable irresolvable dense subspace of . In this model .
Jordan- and Lie geometries
In these lecture notes we report on research aiming at understanding the relation beween algebras and geometries, by focusing on the classes of Jordan algebraic and of associative structures and comparing them with Lie structures. The geometric object sought for, called a generalized projective, resp. an associative geometry, can be seen as a combination of the structure of a symmetric space, resp. of a Lie group, with the one of a projective geometry. The text is designed for readers having basic...
Kikkawa loops and homogeneous loops
In H. Kiechle's publication ``Theory of K-loops'' [3], the name Kikkawa loops is given to symmetric loops introduced by the author in 1973. This concept started from an analogical imagination of sum of vectors in Euclidean space brought up on a sphere. In 1975, this concept was extended by him to the more general concept of homogeneous loops, and it led us to a non-associative generalization of the theory of Lie groups. In this article, the backstage of finding these concepts will be disclosed from...
-groupoids: Algebraic and topological properties of special groupoids. (-Gruppoide: Algebraische und topologische Eigenschaften spezieller Gruppoide.)
Loops and quasigroups: Aspects of current work and prospects for the future
This paper gives a brief survey of certain recently developing aspects of the study of loops and quasigroups, focussing on some of the areas that appear to exhibit the best prospects for subsequent research and for applications both inside and outside mathematics.
Means on scattered compacta
We prove that a separable Hausdor_ topological space X containing a cocountable subset homeomorphic to [0, ω1] admits no separately continuous mean operation and no diagonally continuous n-mean for n ≥ 2.
Multiplikationen mit großen Automorphismengruppen.
Neighborhood base at the identity of free paratopological groups
In 1985, V. G. Pestov described a neighborhood base at the identity of free topological groups on a Tychonoff space in terms of the elements of the fine uniformity on the Tychonoff space. In this paper, we extend Postev’s description to the free paratopological groups where we introduce a neighborhood base at the identity of free paratopological groups on any topological space in terms of the elements of the fine quasiuniformity on the space.
New closure conditions and some problems in loop theory.
No semi topological monoid can be defined on the closure of the set { (x,sin 1 x) : xeR {o...
Note on analytic Moufang loops
It is explicitly shown how the Lie algebras can be associated with the analytic Moufang loops. The resulting Lie algebra commutation relations are well known from the theory of alternative algebras.
On Algebras all of Whose Subalgebras are Simple; Some Solutions of Plonka's Problem
On connected unars with regular endomorphism monoids
On convergence groups with dense coarse subgroups
On free topological algebras
On Functions of Positive Type on Commutative Monoids.
On higher order geometry on anchored vector bundles
Some geometric objects of higher order concerning extensions, semi-sprays, connections and Lagrange metrics are constructed using an anchored vector bundle.
On magnifying elements in grupoids