Extensions of continuous functions into locally convex spaces over non-Archimedean fields
Extensions of functions defined on product spaces
Extensions of functions from products with compact or metric factors
Extensions of G-maps and Euclidean G-retracts.
Extensions of Lebesgue sets and of real-valued functions
Extensions of measurable functions
Extensions of Semicontinuous Multifunctions.
Extensions of Zero-sets and of Real-valued Functions.
Extensions, retracts, and absolute neighborhood retracts in proper shape theory
Factorization theorems for extensions of maps
Fortsetzungen von C...-Funktionen, welche auf einer abgeschlossenen Menge in ...n definiert sind.
Functional characterizations of p-spaces
We show that a completely regular space Y is a p-space (a Čech-complete space, a locally compact space) if and only if given a dense subspace A of any topological space X and a continuous f: A → Y there are a p-embedded subset (resp. a G δ-subset, an open subset) M of X containing A and a quasicontinuous subcontinuous extension f*: M → Y of f continuous at every point of A. A result concerning a continuous extension to a residual set is also given.
Functionally Countable Spaces and Baire Functions
The concept of the distinguished sets is applied to the investigation of the functionally countable spaces. It is proved that every Baire function on a functionally countable space has a countable image. This is a positive answer to a question of R. Levy and W. D. Rice.
Functions with continuous Wallman extensions
Functor of extension in Hilbert cube and Hilbert space
It is shown that if Ω = Q or Ω = ℓ 2, then there exists a functor of extension of maps between Z-sets in Ω to mappings of Ω into itself. This functor transforms homeomorphisms into homeomorphisms, thus giving a functorial setting to a well-known theorem of Anderson [Anderson R.D., On topological infinite deficiency, Michigan Math. J., 1967, 14, 365–383]. It also preserves convergence of sequences of mappings, both pointwise and uniform on compact sets, and supremum distances as well as uniform continuity,...
Functor of extension of -isometric maps between central subsets of the unbounded Urysohn universal space
The aim of the paper is to prove that in the unbounded Urysohn universal space there is a functor of extension of -isometric maps (i.e. dilations) between central subsets of to -isometric maps acting on the whole space. Special properties of the functor are established. It is also shown that the multiplicative group acts continuously on by -isometries.
H-closed functions
The notion of a Hausdorff function is generalized to the concept of H-closed function and the concept of an H-closed extension of a Hausdorff function is developed. Each Hausdorff function is shown to have an H-closed extension.
Hereditarily normal Katětov spaces and extending of usco mappings
Several classes of hereditarily normal spaces are characterized in terms of extending upper semi-continuous compact-valued mappings. The case of controlled extensions is considered as well. Applications are obtained for real-valued semi-continuous functions.
Inductive invariants of closed extensions of mappings
Instability of the eikonal equation and shape from shading
In the shape from shading problem of computer vision one attempts to recover the three-dimensional shape of an object or landscape from the shading on a single image. Under the assumptions that the surface is dusty, distant, and illuminated only from above, the problem reduces to that of solving the eikonal equation |Du|=f on a domain in . Despite various existence and uniqueness theorems for smooth solutions, we show that this problem is unstable, which is catastrophic for general numerical algorithms. ...