Geometry without topology as a new conception of geometry.
Gromov Minimal Fillings for Finite Metric Spaces
Higher-order preconnections in synthetic differential geometry of jet bundles.
Homogeneity properties of hypercubes.
Hyperconvexity of ℝ-trees
It is shown that for a metric space (M,d) the following are equivalent: (i) M is a complete ℝ-tree; (ii) M is hyperconvex and has unique metric segments.
Infinitesimal and local structures for Banach spaces and its exponentials in a topos
Integral distance on a Lipschitz Riemannian manifold.
Isometrien in normierten Räumen.
Isometries on linear -normed spaces.
Logical opens of exponential objects
Mappings which preserve regular dodecahedrons.
Menger curvature and Lipschitz parametrizations in metric spaces
We show that pointwise bounds on the Menger curvature imply Lipschitz parametrization for general compact metric spaces. We also give some estimates on the optimal Lipschitz constants of the parametrizing maps for the metric spaces in Ω(ε), the class of bounded metric spaces E such that the maximum angle for every triple in E is at least π/2 + arcsinε. Finally, we extend Peter Jones's travelling salesman theorem to general metric spaces.
Metric criteria for Banach and Euclidean spaces
Metric Ricci Curvature and Flow for PL Manifolds
We summarize here the main ideas and results of our papers [28], [14], as presented at the 2013 CIRM Meeting on Discrete curvature and we augment these by bringing up an application of one of our main results, namely to solving a problem regarding cube complexes.
Models for synthetic integration theory.
Models for synthetic supergeometry
Necessary and sufficient conditions for unique determination of plane domains.
Nonlinear orthogonal projection
We discuss some properties of an orthogonal projection onto a subset of a Euclidean space. The special stress is laid on projection's regularity and characterization of the interior of its domain.
O čtvrtém Hilbertově problému
O množině středů křivek konstantní křivosti rozšířené hyperbolické roviny, které procházejí daným bodem hyperbolické roviny a dotýkají se dané křivky konstantní křivosti