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1
Content available remote

Un espace métrique linéaire qui n'est pas un rétracte absolu

100%
Cauty R.
Fundamenta Mathematicae
|
1994-1995
|
tom 146
|
nr 1
85-99
FR
We construct the example of the title.
2
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.
3
Content available remote

Sur l’invariance de la dimension infinie forte par t-équivalence

100%
Cauty R.
Fundamenta Mathematicae
|
1999
|
tom 160
|
nr 1
95-100
EN
Let X and Y be metric compacta such that there exists a continuous open surjection from $C_p(Y)$ onto $C_p(X)$. We prove that if there exists an integer k such that $X^k$ is strongly infinite-dimensional, then there exists an integer p such that $Y^p$ is strongly infinite-dimensional.
4
Content available remote

Sur les ouverts des CW-complexes et les fibrés de Serre

100%
Cauty R.
Colloquium Mathematicum
|
1992
|
tom 63
|
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.
5
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.
6
Content available remote

Un exemple de sous-groupe additif de l'espace de Hilbert

100%
Cauty R.
Colloquium Mathematicum
|
1998
|
tom 77
|
nr 1
147-162
7
Content available remote

Suites Fσ -absorbantes en théorie de la dimension

100%
Cauty R.
Fundamenta Mathematicae
|
1999
|
tom 159
|
nr 2
115-126
8
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.
9
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.
10
Content available remote

Sur un exemple de Banach et Kuratowski

100%
Cauty R.
Fundamenta Mathematicae
|
1994
|
tom 144
|
nr 3
195-207
EN
For A ⊂ I = [0,1], let $L_A$ be the set of continuous real-valued functions on I which vanish on a neighborhood of A. We prove that if A is an analytic subset which is not an $F_σ$ and whose closure has an empty interior, then $L_A$ is homeomorphic to the space of differentiable functions from I into ℝ.
11
Content available remote

Ensembles absorbants pour les classes projectives

100%
Cauty R.
Fundamenta Mathematicae
|
1993
|
tom 143
|
nr 3
203-206
EN
We prove the existence, in the Hilbert space, of an absorbing set for the nth projective class.
12
Content available remote

Sur deux espaces de fonctions non dérivables

100%
Cauty R.
Fundamenta Mathematicae
|
1992
|
tom 141
|
nr 3
195-214
EN
Let D (resp. D*) be the subspace of C = C([0,1], R) consisting of differentiable functions (resp. of functions differentiable at the one point at least). We give topological characterizations of the pairs (C, D) and (C, D*) and use them to give some examples of spaces homeomorphic to C\D or to C\D*.
13
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.
14
Content available remote

Un exemple d'ensembles absorbants non équivalents

100%
Cauty R.
Fundamenta Mathematicae
|
1991-1992
|
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.
15
Content available remote

Indépendance linéaire et classification topologique des espaces normés

100%
Cauty R.
Colloquium Mathematicum
|
1993
|
tom 66
|
nr 2
243-255
16
Content available remote

Solution d'un probleme de Fadell sur les fibres

100%
Cauty R.
Colloquium Mathematicum
|
2001
|
tom 90
|
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.
17
Content available remote

Interplay between strongly universal spaces and pairs

70%
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.
18
Content available remote

A homological selection theorem implying a division theorem for Q-manifolds

64%
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.
19
Content available remote

On universality of countable and weak products of sigma hereditarily disconnected spaces

64%
Banakh T., Cauty R.
Fundamenta Mathematicae
|
2001
|
tom 167
|
nr 2
97-109
EN
Suppose a metrizable separable space Y is sigma hereditarily disconnected, i.e., it is a countable union of hereditarily disconnected subspaces. We prove that the countable power $X^{ω}$ of any subspace X ⊂ Y is not universal for the class 𝓐₂ of absolute $G_{δσ}$-sets; moreover, if Y is an absolute $F_{σδ}$-set, then $X^{ω}$ contains no closed topological copy of the Nagata space 𝓝 = W(I,ℙ); if Y is an absolute $G_{δ}$-set, then $X^{ω}$ contains no closed copy of the Smirnov space σ = W(I,0). On the other hand, the countable power $X^{ω}$ of any absolute retract of the first Baire category contains a closed topological copy of each σ-compact space having a strongly countable-dimensional completion. We also prove that for a Polish space X and a subspace Y ⊂ X admitting an embedding into a σ-compact sigma hereditarily disconnected space Z the weak product $W(X,Y) = {(x_i) ∈ X^{ω}: almost all x_i ∈ Y} ⊂ X^{ω}$ is not universal for the class ℳ ₃ of absolute $G_{δσδ}$-sets; moreover, if the space Z is compact then W(X,Y) is not universal for the class ℳ ₂ of absolute $F_{σδ}$-sets.
20
Content available remote

Universalité forte pour les sous-ensembles totalement bornés. Applications aux espaces $C_{p}(X)$

64%
Banakh T., Cauty R.
Colloquium Mathematicum
|
1997
|
tom 73
|
nr 1
25-33
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