A construction of noncontractible simply connected cell-like two-dimensional Peano continua
Using the topologist sine curve we present a new functorial construction of cone-like spaces, starting in the category of all path-connected topological spaces with a base point and continuous maps, and ending in the subcategory of all simply connected spaces. If one starts from a noncontractible n-dimensional Peano continuum for any n > 0, then our construction yields a simply connected noncontractible (n + 1)-dimensional cell-like Peano continuum. In particular, starting from the circle 𝕊¹,...
A note on singularities in ANR's
Completely regular mappings with compact ANR fiber
Concerning locally homotopy negligible sets and characterization of -manifolds
Equiconnectivity and Cofibrations I.
Fixed point index theory for a class of nonacyclic multivalued maps [Book]
Fixed point sets of maps homotopic to a given map.
Fixed point theorems of Rothe-type for Frum-Ketkov- and 1-set-contractions
General position properties in fiberwise geometric topology [Book]
Homological characterization of boundary set complements
La théorie des rétracts approximatifs et le théorème des points fixes de Lefschetz [Book]
Le théorème de Lefschetz pour les ANR approximatifs
Les hyperespaces des rétractes absolus et des rétractes absolus de voisinage du plan
Local cohomological properties of homogeneous ANR compacta
In accordance with the Bing-Borsuk conjecture, we show that if X is an n-dimensional homogeneous metric ANR continuum and x ∈ X, then there is a local basis at x consisting of connected open sets U such that the cohomological properties of Ū and bd U are similar to the properties of the closed ball ⁿ ⊂ ℝⁿ and its boundary . We also prove that a metric ANR compactum X of dimension n is dimensionally full-valued if and only if the group Hₙ(X,X∖x;ℤ) is not trivial for some x ∈ X. This implies that...
Mappings with 1-dimensional absolute neighborhood retract fibers
On a stability theorem for the fixed-point property
On shape and fundamental deformation retracts
On the disjoint (0,N)-cells property for homogeneous ANR's
A metric space (X,ϱ) satisfies the disjoint (0,n)-cells property provided for each point x ∈ X, any map f of the n-cell into X and for each ε > 0 there exist a point y ∈ X and a map such that ϱ(x,y) < ε, and . It is proved that each homogeneous locally compact ANR of dimension >2 has the disjoint (0,2)-cells property. If dimX = n > 0, X has the disjoint (0,n-1)-cells property and X is a locally compact -space then local homologies satisfy for k < n and Hn(X,X-x) ≠ 0.
On the Lefschetz fixed point theorem for multivalued weighted mappings