Wyniki wyszukiwania

1

Size levels for arcs

100%

Sam B. Jr. Nadler, West T.

Fundamenta Mathematicae

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1992

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tom 141

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nr 3

243-255

EN

We determine the size levels for any function on the hyperspace of an arc as follows. Assume Z is a continuum and consider the following three conditions: 1) Z is a planar AR; 2) cut points of Z have component number two; 3) any true cyclic element of Z contains at most two cut points of Z. Then any size level for an arc satisfies 1)-3) and conversely, if Z satisfies 1)-3), then Z is a diameter level for some arc.

2

On the Schauder fixed point theorem

100%

Górniewicz L., Rozpłoch-Nowakowska D.

Banach Center Publications

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1996

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tom 35

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nr 1

207-219

EN

The paper contains a survey of various results concerning the Schauder Fixed Point Theorem for metric spaces both in single-valued and multi-valued cases. A number of open problems is formulated.

3

The space of ANR’s in $ℝ^n$

88%

Dobrowolski T., Rubin L. R.

Fundamenta Mathematicae

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1994-1995

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tom 146

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nr 1

31-58

EN

The hyperspaces $ANR(ℝ^n)$ and $AR(ℝ^n)$ in $2^{ℝ^n} (n ≥ 3)$ consisting respectively of all compact absolute neighborhood retracts and all compact absolute retracts are studied. It is shown that both have the Borel type of absolute $G_{δσ δ}$-spaces and that, indeed, they are not $F_{σ δσ }$-spaces. The main result is that $ANR(ℝ^n)$ is an absorber for the class of all absolute $G_{δσ δ}$-spaces and is therefore homeomorphic to the standard model space $Ω_3$ of this class.

4

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On absolute retracts and absolute convex retracts in some classes of l-groups

75%

Jakubík J.

Discussiones Mathematicae - General Algebra and Applications

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2003

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tom 23

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nr 1

19-30

EN

By dealing with absolute retracts of l-groups we use a definition analogous to that applied by Halmos for the case of Boolean algebras. The main results of the present paper concern absolute convex retracts in the class of all archimedean l-groups and in the class of all complete l-groups.

Ograniczanie wyników

2 Fundamenta Mathematicae

1 Banach Center Publications

1 Discussiones Mathematicae - General Algebra and Applications

1 Dobrowolski T.

1 Górniewicz L.

1 Jakubík J.

1 Rozpłoch-Nowakowska D.

1 Rubin L. R.

1 Sam B. Jr. Nadler

1 West T.

1 2003

1 1996

1 1994

1 1992

Size levels for arcs

On the Schauder fixed point theorem

The space of ANR’s in $ℝ^n$

On absolute retracts and absolute convex retracts in some classes of l-groups