On Extensions of Multivalued Mappings of Topological Spaces
On extensions of uniformly continuous Banach-space-valued mappings
On factorization of maps through τX
On families of large oscillation
On families of Lindelöf and related subspaces of
We consider the families of all subspaces of size ω₁ of (or of a compact zero-dimensional space X of weight ω₁ in general) which are normal, have the Lindelöf property or are closed under limits of convergent ω₁-sequences. Various relations among these families modulo the club filter in are shown to be consistently possible. One of the main tools is dealing with a subspace of the form X ∩ M for an elementary submodel M of size ω₁. Various results with this flavor are obtained. Another tool used...
On fields and ideals connected with notions of forcing
We investigate an algebraic notion of decidability which allows a uniform investigation of a large class of notions of forcing. Among other things, we show how to build σ-fields of sets connected with Laver and Miller notions of forcing and we show that these σ-fields are closed under the Suslin operation.
On filling an irreducible continuum with chainable continua
On filling an irreducible continuum with one point union of 2-cells
On filling an irreducible continuum with the Cartesian product of an arc with a simple triod
On filling an irreducible continuum with the Cartesian product of 1-dimensional continua
On fine shape theory
On fine shape theory II
On finest unitary extensions of topological monoids
We prove that the Wyler completion of the unitary Cauchy space on a given Hausdorff topological 5 monoid consisting of the underlying set of this monoid and of the family of unitary Cauchy filters on it, is a T2-topological space and, in the commutative case, an abstract monoid containing the initial one.
On finite powers of countably compact groups
We will show that under for each there exists a group whose -th power is countably compact but whose -th power is not countably compact. In particular, for each there exists and a group whose -th power is countably compact but the -st power is not countably compact.
On finite sum theorems for transfinite inductive dimensions
We discuss the exactness of estimates in the finite sum theorems for transfinite inductive dimensions trind and trInd. The technique obtained gives an opportunity to repeat and sometimes strengthen some well known results about compacta with trind ≠ trInd. In particular we improve an estimate of the small transfinite inductive dimension of Smirnov’s compacta , given by Luxemburg [Lu2].
On finite -spaces
On finite-dimensional maps and other maps with "small" fibers
We prove that if f is a k-dimensional map on a compact metrizable space X then there exists a σ-compact (k-1)-dimensional subset A of X such that f|X∖A is 1-dimensional. Equivalently, there exists a map g of X in such that dim(f × g)=1. These are extensions of theorems by Toruńczyk and Pasynkov obtained under the additional assumption that f(X) is finite-dimensional. These results are then extended to maps with fibers restricted to some classes of spaces other than the class of k-dimensional...
On finitely equivalent continua.
On finitely Suslinian continua
On fixations of sets in Euclidean spaces