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1
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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.
2
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A function space Cp(X) not linearly homeomorphic to Cp(X) × ℝ

80%
Marciszewski W.
Fundamenta Mathematicae
|
1997
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tom 153
|
nr 2
125-40
EN
We construct two examples of infinite spaces X such that there is no continuous linear surjection from the space of continuous functions $c_p(X)$ onto $c_p(X)$ × ℝ$. In particular, $c_p(X)$ is not linearly homeomorphic to $c_p(X)$ × ℝ$. One of these examples is compact. This answers some questions of Arkhangel'skiĭ.
3
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A contribution to the topological classification of the spaces Ср(X)

80%
Cauty R., Dobrowolski T., Marciszewski W.
Fundamenta Mathematicae
|
1993
|
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 $Ω_α$.
4
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Near metric properties of function spaces

70%
Gartside P. M., Reznichenko E. A.
Fundamenta Mathematicae
|
2000
|
tom 164
|
nr 2
97-114
EN
"Near metric" properties of the space of continuous real-valued functions on a space X with the compact-open topology or with the topology of pointwise convergence are examined. In particular, it is investigated when these spaces are stratifiable or cometrisable.
5
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Multi-valued superpositions

42%
Appell J., Thái N. H., De Pascale E., Zabreĭko P. P.
Instytut Matematyczny Polskiej Akademii Nauk
EN
CONTENTS Introduction.......................................................................................................... 5 1. Multifunctions and selections............................................................................... 7  1. Multifunctions and selections.................................................................. 7  2. Continuous multifunctions and selections........................................... 9  3. Measurable multifunctions and selections............................................ 16 2. Multifunctions of two variables............................................................................... 19  4. Carathéodory multifunctions and selections......................................... 19  5. The Scorza Dragoni property..................................................................... 25  6. Implicit function theorems......................................................................... 32 3. The superposition operator................................................................................... 33  7. The superposition operator in the space S........................................... 34  8. The superposition operator in ideal spaces......................................... 39  9. The superposition operator in the space C........................................... 47 4. Closures and convexifications.............................................................................. 49  10. Strong closures........................................................................................ 49  11. Convexifications....................................................................................... 52  12. Weak closures.......................................................................................... 56 5. Fixed points and integral inclusions..................................................................... 59  13. Fixed point theorems for multi-valued operators................................ 60  14. Hammerstein integral inclusions........................................................ 63  15. A reduction method................................................................................... 68 6. Applications............................................................................................................... 72  16. Applications to elliptic systems.............................................................. 72  17. Applications to nonlinear oscillations................................................. 75  18. Applications to relay problems.............................................................. 78 References.................................................................................................................... 81 Index of symbols........................................................................................................... 93 Index of terms................................................................................................................ 95
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