Open mappings on extremally disconnected compact spaces
Open maps between Knaster continua
We investigate the set of open maps from one Knaster continuum to another. A structure theorem for the semigroup of open induced maps on a Knaster continuum is obtained. Homeomorphisms which are not induced are constructed, and it is shown that the induced open maps are dense in the space of open maps between two Knaster continua. Results about the structure of the semigroup of open maps on a Knaster continuum are obtained and two questions about the structure are posed.
Open maps do not preserve Whyburn property
We show that a (weakly) Whyburn space may be mapped continuously via an open map onto a non (weakly) Whyburn space . This fact may happen even between topological groups and , a homomorphism, Whyburn and not even weakly Whyburn.
Open maps having the Bula property
An open continuous map f from a space X onto a paracompact C-space Y admits two disjoint closed sets F₀,F₁ ⊂ X with f(F₀) = Y = f(F₁), provided all fibers of f are infinite and C*-embedded in X. Applications are given to the existence of "disjoint" usco multiselections of set-valued l.s.c. mappings defined on paracompact C-spaces, and to special type of factorizations of open continuous maps from metrizable spaces onto paracompact C-spaces. This settles several open questions.
Open Maps of Toposes.
Open relations
Open subspaces of countable dense homogeneous spaces
We construct a completely regular space which is connected, locally connected and countable dense homogeneous but not strongly locally homogeneous. The space has an open subset which has a unique cut-point. We use the construction of a -diffeomorphism of the plane which takes one countable dense set to another.
Openly factorizable spaces and compact extensions of topological semigroups
We prove that the semigroup operation of a topological semigroup extends to a continuous semigroup operation on its Stone-Čech compactification provided is a pseudocompact openly factorizable space, which means that each map to a second countable space can be written as the composition of an open map onto a second countable space and a map . We present a spectral characterization of openly factorizable spaces and establish some properties of such spaces.
Opérateurs extrémaux dans certains espaces de Banach
Opérations de Hausdorff itérées et réunions croissantes de compacts
In this paper, motivated by questions in Harmonic Analysis, we study the operation of (countable) increasing union, and show it is not idempotent: iterations are needed in general to obtain the closure of a class under this operation. Increasing union is a particular Hausdorff operation, and we present the combinatorial tools which allow to study the power of various Hausdorff operations, and of their iterates. Besides countable increasing union, we study in detail a related Hausdorff operation,...
Operation-separation axioms in bitopological spaces.
Operator and function spaces which are K-analytic
Operator compactification of topological spaces.
Operator decomposition of continuous mappings.
Operators associated to a topology over a set and related notions.
Operators in normed almost linear spaces
Orbit coupling
Orbit equivalence and Kakutani equivalence with Sturmian subshifts
Using dimension group tools and Bratteli-Vershik representations of minimal Cantor systems we prove that a minimal Cantor system and a Sturmian subshift are topologically conjugate if and only if they are orbit equivalent and Kakutani equivalent.
Orbit spaces of the hyperspace of a graph which are Hilbert cubes
Order and domains of attraction of control sets in flag manifolds.