15 citations · 87 across the 13 of their papers we have counts for
13 papers
Borel complexity of isometry classes of spaces with countable compacta
Marek Cúth, Martin Doležal, Ondřej Kurka +1
For every countable compact space , we determine the exact Borel complexity of the isometry class of the Banach space . As a byproduct, we also determine the pre…
Polish spaces of Banach spaces. Complexity of isometry and isomorphism classes
Marek Cúth, Martin Doležal, Michal Doucha +1
We study the complexities of isometry and isomorphism classes of separable Banach spaces in the Polish spaces of Banach spaces recently introduced and investigated by the authors i…
Projections in Lipschitz-free spaces induced by group actions
Marek Cúth, Michal Doucha
We show that given a compact group acting continuously on a metric space by bi-Lipschitz bijections with uniformly bounded norms, the Lipschitz-free space over the space of…
Characterization of (semi-)Eberlein compacta using retractional skeletons
Claudia Correa, Marek Cúth, Jacopo Somaglia
We deeply study retractions associated to suitable models in compact spaces admitting a retractional skeleton and find several interesting consequences. Most importantly, we provid…
Complexity of distances: Reductions of distances between metric and Banach spaces
Marek Cúth, Michal Doucha, Ondřej Kurka
We show that all the standard distances from metric geometry and functional analysis, such as Gromov-Hausdorff distance, Banach-Mazur distance, Kadets distance, Lipschitz distance,…
Isomorphisms between spaces of Lipschitz functions
Leandro Candido, Marek Cúth, Michal Doucha
We develop tools for proving isomorphisms of normed spaces of Lipschitz functions over various doubling metric spaces and Banach spaces. In particular, we show that $\operatorname{…
Complexity of distances: Theory of generalized analytic equivalence relations
Marek Cúth, Michal Doucha, Ondřej Kurka
We generalize the notion of analytic/Borel equivalence relations, orbit equivalence relations, and Borel reductions between them to their continuous and quantitative counterparts:…
Large separated sets of unit vectors in Banach spaces of continuous functions
Marek Cúth, Benjamin Vejnar, Ondřej Kurka
The paper concerns the problem whether a nonseparable $\C(K)$ space must contain a set of unit vectors whose cardinality equals to the density of $\C(K)$ such that the distances be…
Isometric representation of Lipschitz-free spaces over convex domains in finite-dimensional spaces
Marek Cúth, Ondřej F. K. Kalenda, Petr Kaplický
Let be a finite-dimensional normed space and a nonempty convex open set in . We show that the Lipschitz-free space of is canonically isometric to the quotient of $L^…
Isometric embedding of into Lipschitz-free spaces and into their duals
Marek Cúth, Michal Johanis
We show that the dual of every infinite-dimensional Lipschitz-free Banach space contains an isometric copy of and that it is often the case that a Lipschitz-free Bana…
Monotone retractability and retractional skeletons
Marek Cúth, Ondřej F. K. Kalenda
We prove that a countably compact space is monotonically retractable if and only if it has a full retractional skeleton. In particular, a compact space is monotonically retractable…
Note on Bessaga-Klee classification
Marek Cúth, Ondřej F. K. Kalenda
We collect several variants of the proof of the third case of the Bessaga-Klee relative classification of closed convex bodies in topological vector spaces. We were motivated by th…
Separable reduction theorems by the method of elementary submodels
Marek Cúth
We introduce an interesting method of proving separable reduction theorems - the method of elementary submodels. We are studying whether it is true that a set (function) has given…