Exotic ANR's via null decompositions of Hilbert cube manifolds
Extension of closed mappings
Extension of point-finite partitions of unity
A subspace A of a topological space X is said to be -embedded ((point-finite)-embedded) in X if every (point-finite) partition of unity α on A with |α| ≤ γ extends to a (point-finite) partition of unity on X. The main results are: (Theorem A) A subspace A of X is (point-finite)-embedded in X iff it is -embedded and every countable intersection B of cozero-sets in X with B ∩ A = ∅ can be separated from A by a cozero-set in X. (Theorem B) The product A × [0,1] is (point-finite)-embedded in X...
Extensions of G-maps and Euclidean G-retracts.
Extensions, retracts, and absolute neighborhood retracts in proper shape theory
Fake topological Hilbert spaces and characterizations of dimension in terms of negligibility
Fibering Hilbert cube manifolds over ANRs
Fibrations in the Category of Absolute Neighborhood Retracts
The category Top of topological spaces and continuous maps has the structures of a fibration category and a cofibration category in the sense of Baues, where fibration = Hurewicz fibration, cofibration = the usual cofibration, and weak equivalence = homotopy equivalence. Concentrating on fibrations, we consider the problem: given a full subcategory 𝓒 of Top, is the fibration structure of Top restricted to 𝓒 a fibration category? In this paper we take the special case where 𝓒 is the full subcategory...
Finite-to-one restrictions of continuous functions
Fixed point sets of maps homotopic to a given map.
Fixed point theorems and almost continuity
Fixed point theorems for non-compact approximative ANR's
Free spaces
A space Y is called a free space if for each compactum X the set of maps with hereditarily indecomposable fibers is a dense -subset of C(X,Y), the space of all continuous functions of X to Y. Levin proved that the interval I and the real line ℝ are free. Krasinkiewicz independently proved that each n-dimensional manifold M (n ≥ 1) is free and the product of any space with a free space is free. He also raised a number of questions about the extent of the class of free spaces. In this paper we will...
Function spaces and adjoints.
-variétés topologiques et -microfibrés
G-ANR's with homotopy trivial fixed point sets
Let G be a compact group and X a G-ANR. Then X is a G-AR iff the H-fixed point set is homotopy trivial for each closed subgroup H ⊂ G.
General position properties in fiberwise geometric topology [Book]
Generalized manifolds ANR's and AR's and null decompositions of manifolds
Generalizing the Fixed Point Index.
Homological characterization of boundary set complements