Métriques à entropie topologique positive sur
Metrizability of inverse images of metric spaces under open perfect and 0-dimensional mappings
Metrizable completely distributive lattices
The purpose of this paper is to study the topological properties of the interval topology on a completely distributive lattice. The main result is that a metrizable completely distributive lattice is an ANR if and only if it contains at most finite completely compact elements.
Metrization of D_E[0,1] by Hausdorff distance between graphs
Metrization of function spaces with the Fell topology
For a Tychonoff space , let be the family of hypographs of all continuous maps from to endowed with the Fell topology. It is proved that has a dense separable metrizable locally compact open subset if is metrizable. Moreover, for a first-countable space , is metrizable if and only if itself is a locally compact separable metrizable space. There exists a Tychonoff space such that is metrizable but is not first-countable.
Metrization of Moore spaces and generalized manifolds
Metrization, paracompactness, and real-valued functions
Metrization, paracompactness, and real-valued functions II
Michael's theorem for Lipschitz cells in o-minimal structures
A version of Michael's theorem for multivalued mappings definable in o-minimal structures with M-Lipschitz cell values (M a common constant) is proven. Uniform equi-LCⁿ property for such families of cells is checked. An example is given showing that the assumption about the common Lipschitz constant cannot be omitted.
Minimal bi-Lipschitz embedding dimension of ultrametric spaces
We prove that an ultrametric space can be bi-Lipschitz embedded in if its metric dimension in Assouad’s sense is smaller than n. We also characterize ultrametric spaces up to bi-Lipschitz homeomorphism as dense subspaces of ultrametric inverse limits of certain inverse sequences of discrete spaces.
Minimal class generated by open compact and perfect mappings
Minimal n-prime Ideal Spaces.
Minimal Self-Joinings and Positive Topological Entropy.
Minimal self-joinings and positive topological entropy II
An effective construction of positive-entropy almost one-to-one topological extensions of the Chacón flow is given. These extensions have the property of almost minimal power joinings. For each possible value of entropy there are uncountably many pairwise non-conjugate such extensions.
M-isometries
Mod p Retracts of G-Products Spaces.
Modifications of the double arrow space and related Banach spaces C(K)
We consider the class of compact spaces which are modifications of the well known double arrow space. The space is obtained from a closed subset K of the unit interval [0,1] by “splitting” points from a subset A ⊂ K. The class of all such spaces coincides with the class of separable linearly ordered compact spaces. We prove some results on the topological classification of spaces and on the isomorphic classification of the Banach spaces .
Modules of piecewise polynomials and their freeness.
Monomorphisms and epimorphisms of inverse systems
Monotone approximation of measurable multifunctions by simple multifunctions
We investigate the problem of approximation of measurable multifunctions by monotone sequences of measurable simple ones. Our main tool is the Marczewski function, i.e., the characteristic function of a sequence of sets.