Related papers: Local reflexion spaces

Locally symmetric spaces like $SL(n,\mathbb Z)\backslash SL_n(\mathbb R)/SO(n)$ contain immersed compact flat manifolds of dimension equal to the real rank. We give a lower bound for the contribution of these cycles to the homology of…

We develop the theory of locally small spaces in a new simple language and apply this simplification to re-build the theory of locally definable spaces over structures with topologies.

We give a new proof of a theorem of Loos stating that a Riemannian symmetric space X with rectangular unit lattice is a symmetric R-space. For this we construct explicitly an isometric extrinsically symmetric embedding of X in a Euclidean…

Let M be a transitive model of set theory and X be a space in the sense of M. Is there a reasonable way to interpret X as a space in V? A general theory due to Zapletal provides a natural candidate which behaves well on sufficiently…

L-spaces were introduced by Ozsvath and Szabo using the Heegaard Floer Homology. In the quest for L-spaces we consider links of isolated complete intersection surface singularities. We show that if such a manifold is an L-space, then it is…

This paper concerns the self-similarity of topological spaces, in the sense defined in math.DS/0411344. I show how to recognize self-similar spaces, or more precisely, universal solutions of self-similarity systems. Examples include the…

We consider the question that the spectrum and arithmetic of locally symmetric spaces defined by congruent arithmetical lattices should mutually determine each other. We frame these questions in the context of automorphic representations.

We introduce an abstract definition of a Hamming space that generalizes standard Hamming spaces $( \mathbb{Z}/ 2 \mathbb{Z})^n $. We classify countable locally standard Hamming spaces and show that each of them can be realized as the…

In this paper we will give two different natural generalizations of compact spaces and connected spaces simultaneously. We will show that these generalizations coincide for the subspaces of the real line and that they differ for subspaces…

First, we review local concepts defined previously. A (local) reference frame $\mathrm{F}$ can be defined as an equivalence class of admissible spacetime charts (coordinate systems) having a common domain $\mathrm{U}$ and exchanging by a…

The purpose of this contribution is to give a coherent account of a particular narrative which links locales, geometric theories, sheaf semantics and constructive commutative algebra. We are hoping to convey a firm grasp of three ideas: (1)…

A complete classification of locally spherically symmetric four-dimensional Lorentzian spacetimes is given in terms of their local conformal symmetries. The general solution is given in terms of canonical metric types and the associated…

This paper presents a unified view of manifolds and fiber bundles, which, while superficially different, have strong parallels. It introduces the notions of an m-atlas and of a local coordinate space, and shows that special cases are…

Isaak Moiseevich Yaglom deduced complete classification of geometric spaces. In this work, supposed to your attention, author formalizes Yaglom's approach and constructs uniform theory of geometric spaces on analytic level. Among its…

This paper introduces a notion of generalised geometric logic. Connections of generalised geometric logic with L-topological system and L-topological space are established.

Closure spaces are a generalisation of topological spaces obtained by removing the idempotence requirement on the closure operator. We adapt the standard notion of bisimilarity for topological models, namely Topo-bisimilarity, to closure…

In this thesis we define the notion of a locally stratified space. Locally stratified spaces are particular kinds of streams and d-spaces which are locally modelled on stratified spaces. We construct a locally presentable and cartesian…

We obtain a strengthening of the principle of local reflexivity in a general form. The added strength makes local reflexivity operators respect given subspaces. Applications are given to bounded approximation properties of pairs, consisting…

In this paper, first we give a notion for linear Weingarten spacelike hypersurfaces with $P+aH=b$ in a locally symmetric Lorentz space $L_{1}^{n+1}$. Furthermore, we study complete or compact linear Weingarten spacelike hypersurfaces in…

We investigate the connection between the spatiality of locale products and the earlier studies of the author on the locally fine coreflection of the products of uniform spaces. After giving a historical introduction and indicating the…