Related papers: Building-like spaces

We prove that two dimensional convex subsets of spherical buildings are either buildings or have a center.

In this paper we study convex subcomplexes of spherical buildings. We pay special attention to fixed point sets of type-preserving isometries of spherical buildings. This sets are also convex subcomplexes of the natural polyhedral structure…

In this manuscript the idea of soft convex structures is given and some of their properties are investigated. Also, soft convex sets, soft concave sets and soft convex hull operator are defined and their properties are studied. Moreover,…

For a Euclidean building $X$ of type $A_{2}$, we classify the 0-dimensional subbuildings $A$ of $\partial_{T}X$ that occur as the asymptotic boundary of closed convex subsets. In particular, we show that triviality of the holonomy of a…

A class of Cantor-type spaces and related geometric structures are discussed.

The work consists of solutions of metric problems for convex and finite subsets of geodesic spaces.

We describe various structures of algebraic nature on the space of continuous valuations on convex sets, their properties (like versions of Poincar\'e duality and hard Lefschetz theorem), and their relations and applications to integral…

We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.

Covering space theory is used to construct new examples of buildings.

We introduce notions of concavity for functions on balanced polyhedral spaces, and we show that concave functions on such spaces satisfy several strong continuity properties.

This is a survey on nondiscrete euclidean buildings, with a focus on metric properties of these spaces.

A number of topics involving metrics and measures are discussed, including some of the special structure associated with ultrametrics.

Some boundedness properties of function spaces (considered as topological groups) are studied.

These lectures are an informal elementary introduction to buildings. They are written for, and by, a non-expert. The aim is to get to the definition of a building and feel that it is an entirely natural thing. To maintain the lecture style…

We study the notion of geometric structures for toposes: This generalizes the notion of (X,G) manifolds. We give some applications to algebraic geometry

We define a new structure on a space endowed with convexities, and call it a fractoconvex structure (or, a space with fractoconvexity). We introduce two operations on a set of fractoconvexities and in a special case we show that they…

We investigate several boundedness properties of function spaces considered as uniform spaces.

This is a version of a part of the book ``Transformations of Grassman Spaces'' (in progress). We study transformations of Grassman spaces preserving certain geometrical constructions related to buildings. The next part will be devoted to…

The concept of quasi-partial b-metric-like spaces is being introduced and studied with the help of topology. Examples are also discussed to support the results. Some fixed point theorems are proved in the setting of quasi-partial…

The purpose of this paper is to study the reflections of a convex body. In particular, we are interested in orthogonal reflections of its sections that can be extended to reflections of the whole body. For this reason, we need to study the…