Scientific Seminar
at Geometry and Topology Department of
Ivan Franko National University of Lviv
Archive for (2009/10) academic year



Topology
&
Applications

30.05.10 T. Banakh
  • Non-separable completely metrizable convex subsets of Frechet spaces are homeomorphic to Hilbert spaces
    • We prove that each non-separable completely metrizable convex subset of a Frechet space is homeomorphic to a Hilbert space. This resolves an old (more than 30 years) problem of infinite-dimensional topology. This is a joint work with R.Cauty.
17.05.10 O.Gutik
  • Topological monoids of almost monotone injective cofinite partial selfmaps of positive integers
    • We describe the algebraic structure of the semigroup of almost monotone injective cofinite partial selfmaps of the set of positive integers and discuss its topologizings as a topological (semitopological) semigroup.
26.04.10 T.Banakh
  • On functors with finite supports
    • We prove that a monomorphic functor F:CompComp with finite supports is epimorphic, continuous, and its maximal ∅-modification Fo preserves intersections. This implies that a monomorphic functor F:CompComp of finite degree deg F≤n preserves (finite-dimensional) compact ANRs if the spaces F∅, Fo∅, and Fn are finite-dimensional ANRs. This improves a known result of Basmanov.
19.04.10 O.Nykyforchyn
  • Functors of fuzzy representations
    • We detect topological spaces X whose space SCp(X) of scatteredly continuous functions is not normal or has uncountable extent. In particular, we prove that the space SCp(X) over a compact Hausdorff space X is normal if and only if X is countable.
12.04.10 O.Savchenko
  • Fuzzy metrics and functors
22.03.10
29.03.10
N.Kolos
  • Extent and normality of the spaces of scatteredly continuous functions
    • We detect topological spaces X whose space SCp(X) of scatteredly continuous functions is not normal or has uncountable extent. In particular, we prove that the space SCp(X) over a compact Hausdorff space X is normal if and only if X is countable.
15.03.09 Yevgen Olin
(Kharkiv)
  • Some comparison theorems for convex surfaces in Finsler spaces of non-positive flag curvature
    • In the talk we consider locally convex hypersurfaces in Finsler and Hilbert geometries. We prove that under certain conditions immersed hypersurface in non-positively curved Finsler space is embedded as the boundary of convex body. We estimate the ratio of the volume of metric ball to the area of metric sphere in Finsler and Hilbert geometries. We obtain that the normal curvatures, Finsler curvature and Rund cuvature of hyperspheres in Hilbert geometry tend to 1 as radius tend to infinity.
1.03.09 M.Zarichnyi
  • A sketch of mathematical biography of Igor Guran
    • We shall explain principal mathematical results of I.I.Guran.
15.02.09
22.02.09
All
  • Divertissement
    • The active participants of the topological seminar will discuss new results and pose some open problems.
  • Winter Holydays
28.12.09 O.Hubal'
  • Capacites on ultrametric spaces
    • The talk is devoted to a counterpart of a construction due to Hartog and Ruffen of ultrametrization of the space of upper-semicontinuous capacities (non-additive measures) of compact supports defined on ultrametric spaces.
21.12.09 T.Banakh
  • The functors Eω of uniform functionals in the category of compact Hausdorff spaces
    • We shall define a family of weakly normal functors Eω in the category of compact Hausdorff spaces and discuss the metrizability problem for such functors. A functor Eω is parametrized by a function ω called a continuity modulus. As a particular case of this construction we obtain the functor E of non-expanding functionals and the functors Ek of k-Lipschitz functionals.
14.12.09 T.Banakh
  • Zariski topologies on groups
    • The n-th Zariski topology on a group G is generated by the subbase consisting of the sets {x: p(x)≠1} where p(x) is a monomial of degree ≤n on G. The 0th Zariski topology on G is antidiscrete while the first Zariski topology on G is cofinite. We prove that the 2-nd Zariski topology on each infinite group is non-discrete. On the other hand, the 665-th Zariski topology of the Olshanskii non-topologizable group G is disctrete. Also we construct an example of a group of cardinality continuum whose second ZAriski topology has countable pseudocharacter.
      This is a joint work with I.Protasov.
07.12.09 L.Karchevska
  • Infinite-dimensional bundles in the topology of monad O
    • We show that the multiplication map of the monad O is a trivial bundle whose fibers are homeomorphic to an infinite-dimensional cube.
23.11.09
30.11.09
M.Zarichnyi
  • Universal spaces for fuzzy metric spaces
    • We discuss the existence of a universal space in the class of fuzzy metric spaces.
16.11.09 O.Ravsky
  • Reversivity of subsemigroups of topological groups
    • We discuss the problem of reversivity of an open subsemigroup of a connected topological group. We recall that a semigroup S is left reversive if for any points x,y of S the intersection of the ideals xS and yS is not empty.
      This is a joint work with I.Guran.
09.11.09 T.Banakh
  • Manifolds admitting a continuous cancellative operation are orientable.
    • We prove that a topological manifold M (possibly with boundary) is orientable if M admits a continuous cancellative binary operation.
26.10.09 T.Radul
  • Hyperspaces of B-convex compacta.
    • We study the topological structure of the hyperspace of B-convex compacta in a metric space. A subset C of a metric space X is called B-convex if for any finite subset F of X the intersection of all balls that contain F lies in C. In particular, we characterize (finite-dimensional) Banach spaces whose hyperspace of B-convex compacta is homeomorphic to the Hilbert cube with one removed point.
19.10.09 I.Zarichnyi
  • Detecting metric spaces that are coarsely equivalent to the anti-Cantor set.
    • We shall detect some metric spaces that are coarsely equivalent to the anti-Cantor set 2. In particular, we show that the space {n2}n x 2 is coarsely equivalent to the anti-Cantor set 2.
12.10.09 V.Kruglov (Kharkiv)
  • Parabolic and saddle foliations and distributions on 3-dimensional manifolds
    • В роботі вивчаються контактні структури та шарування на замкнених тривимірних многовидах, що мають обмеження на зовнішню, секційну або Гаусову кривини розподілення. Доведені теореми існування шарувань з обмеженням на зовнішню кривину. Доведена теорема про "уніформізацію" контактних структур: кожна контактна структура на замкненому тривимірному многовиді має постійну секційну (Гаусову) кривину відносно деякої метрики. Показано, що всі контактні структури є параболічними відносно деякої метрики. Якщо клас Ейлера контактної структури дорівнює нулю, доведено, що контактна структура є сідловою.
28.09.09
05.10.09
T.Banakh
  • The hyperspaces Bdd(Q) and Bdd(Q2) are not homeomorphic.
    • We discuss topological properties of the hyperspace Bdd(X) of closed bounded subsets of a metric space X, endowed with the Hausdorff metric. In particular, we prove that the hyperspaces Bdd(Qn), n≥2, are pairwise homeomorphic, while the hyperspaces Bdd(Q) and Bdd(Q2) are non-homeomorphic. This resolves a problem from the book "Open Problems in Topology, II".
      This is a joint work with R.Cauty.
21.09.09 R.Cauty (Paris)
  • Infinite-dimensional topology of hyperspaces
    • Theoreme 1. Soient X un espace metrique connexe, localement connexe non compact, et d une distance sur X telle que tout ferme borne soit compact. Soit G un sous-ensemble de X de type Gδ tel que G et X\G soient dense . Alors le couple (Bbb X, Bbb G) est homeomorphe a (Q,s)\{point}.
14.09.09 All
  • Divertissement
    • The active participants of the topological seminar will discuss new results and pose some open problems.