Mappings with 1-dimensional absolute neighborhood retract fibers
Maps with dimensionally restricted fibers
We prove that if f: X → Y is a closed surjective map between metric spaces such that every fiber belongs to a class S of spaces, then there exists an -set A ⊂ X such that A ∈ S and for all y ∈ Y. Here, S can be one of the following classes: (i) M: e-dim M ≤ K for some CW-complex K; (ii) C-spaces; (iii) weakly infinite-dimensional spaces. We also establish that if S = M: dim M ≤ n, then dim f ∆ g ≤ 0 for almost all .
Mesures de Gibbs sur les Cantor réguliers
Metric dimension and equivalent metrics
Metrische Dimensionsfunktionen.
Minimal bi-Lipschitz embedding dimension of ultrametric spaces
We prove that an ultrametric space can be bi-Lipschitz embedded in if its metric dimension in Assouad’s sense is smaller than n. We also characterize ultrametric spaces up to bi-Lipschitz homeomorphism as dense subspaces of ultrametric inverse limits of certain inverse sequences of discrete spaces.
Neighborhoods of compacta in euclidean space
Note on metric-dependent dimension functions
Notes on Retracts of Coset Spaces
We study retracts of coset spaces. We prove that in certain spaces the set of points that are contained in a component of dimension less than or equal to n, is a closed set. Using our techniques we are able to provide new examples of homogeneous spaces that are not coset spaces. We provide an example of a compact homogeneous space which is not a coset space. We further provide an example of a compact metrizable space which is a retract of a homogeneous compact space, but which is not a retract of...
n-шейпы и n-когомотопические группы компактов
O dimenziji P-dm topoloških prostora
On a construction of perfectly normal spaces and its applications to dimension theory
On a construction of universal hereditarily indecomposable continua based on the Baire category
We give a proof of a theorem of Maćkowiak on the existence of universal n-dimensional hereditarily indecomposable continua, based on the Baire-category method.
On a question of de Groot and Nishiura
Let . Then cmp Zₙ < def Zₙ for n ≥ 5. This is the answer to a question posed by de Groot and Nishiura [GN] for n ≥ 5.
On a special metric and dimension
On a theorem of P. S. Aleksandrov
On a theorem of W. Hurewicz on mappings which lower dimension
On analytical dimension of rings of bounded uniformly continuous functions
On Applications of Bing-Krasinkiewicz-Lelek Maps
We characterize Peano continua using Bing-Krasinkiewicz-Lelek maps. Also we deal with some topics on Whitney preserving maps.
On approximate inverse systems and resolutions