The transposition of locally compact, connected translation planes

Sixteen-dimensional Locally Compact Translation Planes Admitting Sl2 H as a Group of Collineations

In this paper, all 16-dimensional locally compact translation planes admitting the unimodular quaternion group SL2H as a group of collineations will be determined explicitly. Besides the classical plane over the octonions there are a vast number of planes having this property, cf. the Classification Theorem (2.8). Indeed, the class of these planes covers an interesting borderline case: Among al...

Finitely generated connected locally compact groups

Hofmann and Morris [6] proved that a locally compact connected group G has a finite subset generating a dense subgroup if and only if the weight w(G) of G does not exceed c , the cardinality of the continuum. The minimum cardinality of such a topological generating set is an invariant of the group, is denoted by σ(G), and is called the topological rank of G . For compact abelian groups of weigh...

The existence of Zak transform in locally compact hypergroups

Let K be a locally compact hypergroup. In this paper we initiate the concept of fundamental domain in locally compact hypergroups and then we introduce the Borel section mapping. In fact, a fundamental domain is a subset of a hypergroup K including a unique element from each cosets, and the Borel section mapping is a function which corresponds to any coset, the related unique element in the fun...

On planarity of compact, locally connected, metric spaces

Thomassen [Combinatorica 24 (2004), 699–718] proved that a 2–connected, compact, locally connected metric space is homeomorphic to a subset of the sphere if and only if it does not contain K5 or K3,3. The “thumbtack space” consisting of a disc plus an arc attaching just at the centre of the disc shows the assumption of 2–connectedness cannot be dropped. In this work, we introduce “generalized t...

P-Amenable Locally Compact Hypergroups