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1
Content available remote Solution du problème de point fixe de Schauder
100%
Cauty R.
Fundamenta Mathematicae
|
2001
|
tom 170
|
nr 3
231-246
EN
We give an affirmative answer to Schauder's fixed point question.
2
Content available remote Sur les ouverts des CW-complexes et les fibrés de Serre
100%
Cauty R.
|
|
nr 1
1-7
FR
M. Steinberger et J. West ont prouvé dans [7] qu'un fibré de Serre p:E → B entre CW-complexes a la propriété de relèvement des homotopies par rapport aux k-espaces. Malheureusement, leur démonstration contient une légère erreur. Ils affirment que certains ensembles (notés U et $p^{-1}U×U$) sont des CW-complexes car ce sont des ouverts de CW-complexes. Ceci est généralement faux, et notre premier objectif dans cette note est de donner des exemples d'ouverts de CW-complexes n'admettant aucune décomposition CW. Malgré cela, le théorème de Steinberger et West est vrai, et notre deuxième objectif est de montrer comment leur démonstration peut être rectifiée.
3
Content available remote Diagrammes cocartésiens et rétractes absolus de voisinage
100%
Cauty R.
Colloquium Mathematicum
|
2004
|
tom 101
|
nr 2
143-154
EN
We solve a problem of Dranishnikov about pushouts of ANRs.
4
Content available remote Solution d'un probleme de Fadell sur les fibres
100%
Cauty R.
|
|
nr 2
151-157
EN
Let E be the total space of a Hurewicz fiber space whose base and all fibers are ANRs. We prove that if E is metrisable, then it is also an ANR.
5
Content available remote Un exemple d'ensembles absorbants non équivalents
100%
Cauty R.
|
|
tom 140
|
nr 1
49-61
EN
We give an example in the Hilbert space $ℓ^2$ of two subsets which are absorbing for the class of topologically complete spaces, but for which there exists no homeomorphism of $ℓ^2$ onto itself mapping one of these subsets onto the other.
6
Content available remote Une caractérisation des rétractes absolus de voisinage
100%
Cauty R.
Fundamenta Mathematicae
|
1994
|
tom 144
|
nr 1
11-22
FR
We prove that a metric space is an ANR if, and only if, every open subset of X has the homotopy type of a CW-complex.
7
Content available remote Homologie des groupes et généralisations du théorème de Borsuk-Ulam
100%
Cauty R.
Colloquium Mathematicum
|
2007
|
tom 108
|
nr 1
119-134
EN
We show that many generalisations of Borsuk-Ulam's theorem follow from an elementary result of homological algebra.
8
Content available remote Sur les rétractes absolus Pn -valués de dimension finie
100%
Cauty R.
Fundamenta Mathematicae
|
1998
|
tom 158
|
nr 3
241-248
EN
We prove that a k-dimensional hereditarily indecomposable metrisable continuum is not a $P_k$-valued absolute retract. We deduce from this that none of the classical characterizations of ANR (metric) extends to the class of stratifiable spaces.
9
Content available remote Un espace métrique linéaire qui n'est pas un rétracte absolu
100%
Cauty R.
|
|
tom 146
|
nr 1
85-99
FR
We construct the example of the title.
10
Content available remote Indépendance linéaire et classification topologique des espaces normés
100%
Cauty R.
Colloquium Mathematicum
|
1993
|
tom 66
|
nr 2
243-255
11
Content available remote Interplay between strongly universal spaces and pairs
72%
Banakh T. , Cauty R.
Instytut Matematyczny Polskiej Akademii Nauk
EN
Given a pair (M,X) of spaces we investigate the connections between the (strong) universality of (M,X) and that of the space X. We apply this to prove Enlarging, Deleting, and Strong Negligibility Theorems for strongly universal and absorbing spaces. Given an absorbing space Ω we also study the question of topological uniqueness of the pair (M,X), where $M = [0,1]^{ω}$ or $M = (0,1)^{ω}$ and X is a copy of Ω in M having a locally homotopy negligible complement in M.
12
Content available remote Universalité forte pour les sous-ensembles totalement bornés. Applications aux espaces $C_{p}(X)$
63%
Banakh T. , Cauty R.
Colloquium Mathematicum
|
1997
|
tom 73
|
nr 1
25-33
13
Content available remote A homological selection theorem implying a division theorem for Q-manifolds
63%
Banakh T. , Cauty R.
Banach Center Publications
|
2007
|
tom 77
|
nr 1
11-22
EN
We prove that a space M with Disjoint Disk Property is a Q-manifold if and only if M × X is a Q-manifold for some C-space X. This implies that the product M × I² of a space M with the disk is a Q-manifold if and only if M × X is a Q-manifold for some C-space X. The proof of these theorems exploits the homological characterization of Q-manifolds due to Daverman and Walsh, combined with the existence of G-stable points in C-spaces. To establish the existence of such points we prove (and afterward apply) homological versions of the Brouwer Fixed Point Theorem and of Uspenskij's Selection Theorem.
14
Content available remote Topological classification of closed convex sets in Fréchet spaces
63%
Banakh T. , Cauty R.
|
|
nr 1
1-11
EN
We prove that each non-separable completely metrizable convex subset of a Fréchet space is homeomorphic to a Hilbert space. This resolves a more than 30 years old problem of infinite-dimensional topology. Combined with the topological classification of separable convex sets due to Klee, Dobrowolski and Toruńczyk, this result implies that each closed convex subset of a Fréchet space is homeomorphic to $[0,1]ⁿ × [0,1)^{m} × ℓ₂(κ)$ for some cardinals 0 ≤ n ≤ ω, 0 ≤ m ≤ 1 and κ ≥ 0.
15
Content available remote On universality of finite powers of locally path-connected meager spaces
63%
Banakh T. , Cauty R.
|
|
tom 102
|
nr 1
87-95
EN
It is shown that for every integer n the (2n+1)th power of any locally path-connected metrizable space of the first Baire category is 𝓐₁[n]-universal, i.e., contains a closed topological copy of each at most n-dimensional metrizable σ-compact space. Also a one-dimensional σ-compact absolute retract X is found such that the power X^{n+1} is 𝓐₁[n]-universal for every n.
16
Content available remote A contribution to the topological classification of the spaces Ср(X)
51%
Cauty R. , Dobrowolski T. , Marciszewski W.
|
|
tom 142
|
nr 3
269-301
EN
We prove that for each countably infinite, regular space X such that $C_p(X)$ is a $Z_σ$-space, the topology of $C_p(X)$ is determined by the class $F_0(C_p(X))$ of spaces embeddable onto closed subsets of $C_p(X)$. We show that $C_p(X)$, whenever Borel, is of an exact multiplicative class; it is homeomorphic to the absorbing set $Ω_α$ for the multiplicative Borel class $M_α$ if $F_0(C_p(X)) = M_α$. For each ordinal α ≥ 2, we provide an example $X_α$ such that $C_p(X_α)$ is homeomorphic to $Ω_α$.
17
Content available remote Sur le prolongement des fonctions continues dans les complexes simpliciaux infinis
51%
Cauty R.
Fundamenta Mathematicae
|
1990
|
tom 134
|
nr 3
221-245
18
Content available remote Les fonctions continues et les fonctions intégrables au sens de Riemann comme sous-espaces de $ℒ^1$
51%
Cauty R.
Fundamenta Mathematicae
|
1991
|
tom 139
|
nr 1
23-36
19
Content available remote Les hyperespaces des rétractes absolus et des rétractes absolus de voisinage du plan
45%
Cauty R. , Dobrowolski T. , Gladdines H. , van Mill J.
Fundamenta Mathematicae
|
1995
|
tom 148
|
nr 3
257-282
20
Content available remote Caractérisation topologique de l'espace des fonctions dérivables
38%
Cauty R.
Fundamenta Mathematicae
|
1991
|
tom 138
|
nr 1
35-58
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