Related papers: On two methods of constructing compactifications o…
The survey contains a brief description of the ideas, constructions, results, and prospects of the theory of hypergroups and generalized translation operators. Representations of hypergroups are considered, being treated as continuous…
By introducing various topologies on the homotopy groups of a topological space, some researchers make these well known notions in algebraic topology more useful and powerful. In this paper, first we recall and review some known topologies…
In finite graphs, finite-order tangles offer an abstract description of highly connected substructures. In infinite graphs, infinite-order tangles compactify the graphs in the same way the ends compactify connected locally finite graphs.…
We study locally compact group topologies on semisimple Lie groups. We show that the Lie group topology on such a group $S$ is very rigid: every 'abstract' isomorphism between $S$ and a locally compact and $\sigma$-compact group $\Gamma$ is…
Let $H$ be a group and $E$ a set such that $H \subseteq E$. We shall describe and classify up to an isomorphism of groups that stabilizes $H$ the set of all group structures that can be defined on $E$ such that $H$ is a subgroup of $E$. A…
We consider a version of the notion of F-inverse semigroup (studied in the algebraic theory of inverse semigroups). We point out that an action of such an inverse semigroup on a locally compact space has associated a natural groupoid…
We discuss the problem of finding an analogue of the concept of a topological space in supergeometry, motivated by a search for a procedure to compactify a supermanifold along odd coordinates. In particular, we examine the topologies…
We study, as hypersurfaces in toric varieties, elliptic Calabi-Yau fourfolds for F-theory compactifications dual to E8xE8 heterotic strings compactified to four dimensions on elliptic Calabi-Yau threefolds with some choice of vector bundle.…
A vector topology on a vector space over a topological field is a (not necessarily Hausdorff) topology by which the addition and scalar multiplication are continuous. We prove that, if an isomorphism between the lattice of topologies of two…
In this paper we consider the classification of minimal cellular structures of spaces of topological complexity two under some hypotheses on there graded cohomological algebra. This continues the method used by M.Grant et al. in [1].
Borrowing ideas from elliptic complex geometry, we approach M-theory compactifications on real toric fibrations. Precisely, we explore real toric equations rather than complex ones exploited in F-theory and related dual models. These…
For real application and theoretical investigation of ordinary hypergraphs and non-ordinary hypergraphs, researchers need to establish standard rules and feasible operating methods. We propose a visualization tool for investigating…
In a series of three papers we develop an end space theory for digraphs. Here in the second paper we introduce the topological space $|D|$ formed by a digraph $D$ together with its ends and limit edges. We then characterise those digraphs…
We investigate the construction and properties of Clifford algebras by a similar manner as our previous construction of the octonions, namely as a twisting of group algebras of Z_2^n by a cocycle. Our approach is more general than the usual…
In this paper it is proven that if the group of covering translations of the covering space of a compact, connected, $P^2$-irreducible 3-manifold corresponding to a non-trivial, finitely-generated subgroup of its fundamental group is…
We present a way of topologizing sets of Galois types over structures in abstract elementary classes with amalgamation. In the elementary case, the topologies thus produced refine the syntactic topologies familiar from first order logic. We…
For Pontryagin's group duality in the setting of locally compact topological Abelian groups, the topology on the character group is the compact open topology. There exist at present two extensions of this theory to topological groups which…
Given any arbitrary semi-algebraic set $X$, any two points in $X$ may be joined by a piecewise $C^2$ path $\gamma$ of shortest length. Suppose $\mathcal{A}$ is a semi-algebraic stratification of $X$ such that each component of $\gamma \cap…
In contrast to classical strongly continuous semigroups, the study of bi-continuous semigroups comes with some freedom in the properties of the associated locally convex topology. This paper aims to give minimal assumptions in order to…
Group contraction is an algebraic map that relates two classes of Lie groups by a limiting process. We utilize this notion for the compactification of the class of Cartan motion groups. The compactification process is then applied to reduce…