

30.05.10

T. Banakh


Nonseparable completely metrizable convex subsets of Frechet spaces are
homeomorphic to Hilbert spaces

We prove that each nonseparable completely metrizable convex subset of a
Frechet space is homeomorphic to a Hilbert space.
This resolves an old (more than 30 years) problem of infinitedimensional
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:Comp→Comp with finite supports is epimorphic,
continuous, and its maximal
∅modification F^{o} preserves intersections.
This implies that a monomorphic functor F:Comp→Comp
of finite degree deg F≤n
preserves (finitedimensional) compact ANRs if the spaces
F∅, F^{o}∅, and Fn are finitedimensional ANRs.
This improves a known result of Basmanov.







19.04.10

O.Nykyforchyn


Functors of fuzzy representations

We detect topological spaces X whose space SC_{p}(X) of scatteredly
continuous functions is not normal or has uncountable extent.
In particular, we prove that the space SC_{p}(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 SC_{p}(X) of scatteredly
continuous functions is not normal or has uncountable extent.
In particular, we prove that the space SC_{p}(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 nonpositive flag curvature

In the talk we consider locally convex hypersurfaces in Finsler and Hilbert geometries.
We prove that under certain conditions immersed hypersurface
in nonpositively 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.








 






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 uppersemicontinuous capacities
(nonadditive measures) of compact supports defined on ultrametric spaces.







21.12.09

T.Banakh


The functors E_{ω} of uniform functionals in the category of compact Hausdorff spaces

We shall define a family of weakly normal functors E_{ω} in the category of compact Hausdorff spaces and discuss
the metrizability problem for such functors. A functor E_{ω} is parametrized by a function ω
called a continuity modulus. As a particular case of this construction we obtain the functor E of nonexpanding
functionals and the functors E_{k} of kLipschitz functionals.







14.12.09

T.Banakh


Zariski topologies on groups

The nth 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 2nd Zariski topology on each infinite group is nondiscrete.
On the other hand, the 665th Zariski topology of the Olshanskii nontopologizable 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


Infinitedimensional 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 infinitedimensional 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 Bconvex compacta.

We study the topological structure of the hyperspace of Bconvex compacta in a metric space.
A subset C of a metric space X is called Bconvex if for any finite subset F of X the intersection of all balls that contain F lies in C.
In particular, we characterize (finitedimensional) Banach spaces whose hyperspace of Bconvex 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 antiCantor set.

We shall detect some metric spaces that are coarsely equivalent to the antiCantor set 2^{<ω}. In particular, we show that the space {n^{2}}_{n} x 2^{<ω} is coarsely equivalent to the antiCantor set 2^{<ω}.







12.10.09

V.Kruglov
(Kharkiv)


Parabolic and saddle foliations and distributions on 3dimensional 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(Q^{2}) are not homeomorphic.







21.09.09

R.Cauty
(Paris)


Infinitedimensional 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 sousensemble de X de type G_{δ} 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.





