Maximality principle and general results of Ekeland and Caristi types without lower semicontinuity assumptions in cone uniform spaces with generalized pseudodistances.
Mean dimension, small entropy factors and an embedding theorem
Means on scattered compacta
We prove that a separable Hausdor_ topological space X containing a cocountable subset homeomorphic to [0, ω1] admits no separately continuous mean operation and no diagonally continuous n-mean for n ≥ 2.
Measurability of equivalence classes and MEC-property in metric spaces.
Measurability of some sets of Borel measurable functions on .
Measurable functionals on function spaces
We prove that all measurable functionals on certain function spaces are measures; this improves the (known) results about weak sequential completeness of spaces of measures. As an application, we prove several results of this form: if the space of invariant functionals on a function space is separable then every invariant functional is a measure.
Measurable Refinement Monoids and Applications to Distributive Semilattices, Heyting Algebras, and Stone Spaces.
Measurable uniform spaces
Measure theoretic zero sets in infinite dimensional spaces and differentiability of Lipschitz mappings
Medias generalizadas y aplicaciones.
Meir-Keeler contractions of integral type are still Meir-Keeler contractions.
Menger's Theorem for topological spaces
Merging of degree and index theory.
Metric spaces admitting only trivial weak contractions
If (X,d) is a metric space then a map f: X → X is defined to be a weak contraction if d(f(x),f(y)) < d(x,y) for all x,y ∈ X, x ≠ y. We determine the simplest non-closed sets X ⊆ ℝⁿ in the sense of descriptive set-theoretic complexity such that every weak contraction f: X → X is constant. In order to do so, we prove that there exists a non-closed set F ⊆ ℝ such that every weak contraction f: F → F is constant. Similarly, there exists a non-closed set G ⊆ ℝ such that every weak contraction...
Metric spaces in which a strengthened form of Blumberg's theorem holds
Metric-fine, proximally fine, and locally fine uniform spaces
Metrizable groups and strict o-boundedness
Minimal actions of homeomorphism groups
Let X be a closed manifold of dimension 2 or higher or the Hilbert cube. Following Uspenskij one can consider the action of Homeo(X) equipped with the compact-open topology on , the space of maximal chains in , equipped with the Vietoris topology. We show that if one restricts the action to M ⊂ Φ, the space of maximal chains of continua, then the action is minimal but not transitive. Thus one shows that the action of Homeo(X) on , the universal minimal space of Homeo(X), is not transitive (improving...
Minimal and distal functions on semidirect products of groups
Minimal component numbers of fixed point sets
Let f: (X,A) → (X,A) be a relative map of a pair of compact polyhedra. We introduce a new relative homotopy invariant , which is a lower bound for the component numbers of fixed point sets of the self-maps in the relative homotopy class of f. Some properties of are given, which are very similar to those of the relative Nielsen number N(f;X,A).