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Algebraic aspects of web geometry

Maks A. Akivis, Vladislav V. Goldberg (2000)

Commentationes Mathematicae Universitatis Carolinae

Algebraic aspects of web geometry, namely its connections with the quasigroup and loop theory, the theory of local differential quasigroups and loops, and the theory of local algebras are discussed.

Cardinalities of lattices of topologies of unars and some related topics

Anna Kartashova (2001)

Discussiones Mathematicae - General Algebra and Applications

In this paper we find cardinalities of lattices of topologies of uncountable unars and show that the lattice of topologies of a unar cannor be countably infinite. It is proved that under some finiteness conditions the lattice of topologies of a unar is finite. Furthermore, the relations between the lattice of topologies of an arbitrary unar and its congruence lattice are established.

Connected LCA groups are sequentially connected

Shou Lin, Mihail G. Tkachenko (2013)

Commentationes Mathematicae Universitatis Carolinae

We prove that every connected locally compact Abelian topological group is sequentially connected, i.e., it cannot be the union of two proper disjoint sequentially closed subsets. This fact is then applied to the study of extensions of topological groups. We show, in particular, that if H is a connected locally compact Abelian subgroup of a Hausdorff topological group G and the quotient space G / H is sequentially connected, then so is G .

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