5 citations · 14 across the 7 of their papers we have counts for
11 papers
On sets where lip(f) is infinite for monotone continuous functions
Martin Rmoutil, Thomas Zürcher
Given an F-sigma-delta subset A of the real line R of Lebesgue measure zero, we construct a monotone absolutely continuous function f from R to R such that the little Lipschitz con…
On sets where is finite
Zoltán Buczolich, Bruce Hanson, Martin Rmoutil +1
Given a function , the so-called "little lip" function is defined as follows: \begin{equation*} \operatorname{lip} f(x)=\li…
Restricting uniformly open surjections
Tomasz Kania, Martin Rmoutil
We employ the theory of elementary submodels to improve a recent result by Aron, Jaramillo and Le Donne (Ann. Acad. Sci. Fenn. Math., to appear) concerning restricting uniformly op…
Recovering a compact Hausdorff space from the compatibility ordering on
Tomasz Kania, Martin Rmoutil
Let and be scalar-valued, continuous functions on some topological space. We say that dominates in the compatibility ordering if coincides with on the suppo…
Haar meager sets revisited
Martin Doležal, Martin Rmoutil, Benjamin Vejnar +1
In the present article we investigate Darji's notion of Haar meager sets from several directions. We consider alternative definitions and show that some of them are equivalent to t…
Norm-attaining functionals and proximinal subspaces
Martin Rmoutil
G. Godefroy asked whether, on any Banach space, the set of norm-attaining functionals contains a 2-dimensional linear subspace. We prove that a recent construction due to C.J. Read…
On Separable Determination of Sigma-P-Porous Sets in Banach Spaces
Marek Cuth, Martin Rmoutil, Miroslav Zeleny
We use a method involving elementary submodels and a partial converse of Foran lemma to prove separable reduction theorems concerning Suslin sigma-P-porous sets where "P" can be fr…
On Removable Sets For Convex Functions
Dusan Pokorny, Martin Rmoutil
In the present article we provide a sufficient condition for a closed set F in R^d to have the following property which we call c-removability: Whenever a function f:R^d->R is loca…
On the nonexistence of a relation between σ-left-porosity and σ-right-porosity
Martin Rmoutil
Given an arbitrarily weak notion of left-<f>-porosity and an arbitrarily strong notion of right-<g>-porosity, we construct an example of closed subset of the real line which is not…
Products of non-sigma-lower porous sets
Martin Rmoutil
It has been known that the Cartesian product of two Suslin non-sigma-porous sets in topologically complete metric spaces is non-sigma-porous in the product space. The main aim of t…
Sigma-porosity is separably determined
Marek Cúth, Martin Rmoutil
We prove a separable reduction theorem for sigma-porosity of Suslin sets. In particular, if A is a Suslin subset in a Banach space X, then each separable subspace of X can be enlar…