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1
Content available remote 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
Content available remote A Ramsey theorem for polyadic spaces
100%
Bell M. G.
Fundamenta Mathematicae
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1996
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tom 150
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nr 2
189-195
EN
A polyadic space is a Hausdorff continuous image of some power of the one-point compactification of a discrete space. We prove a Ramsey-like property for polyadic spaces which for Boolean spaces can be stated as follows: every uncountable clopen collection contains an uncountable subcollection which is either linked or disjoint. One corollary is that $(ακ)^ω$ is not a universal preimage for uniform Eberlein compact spaces of weight at most κ, thus answering a question of Y. Benyamini, M. Rudin and M. Wage. Another consequence is that the property of being polyadic is not a regular closed hereditary property.
3
Content available remote Correcting theorem 1 from "When lines go bad in hyperspace"
100%
Schlicker S. , Bay C. , Lembcke A.
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2009
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tom Vol. 42, nr 2
237-240
EN
This is in regards to the paper "When Lines go bad in hyperspace" by Christopher Bay, Amber Lembcke, and Steven Schlicker which appears in Demonstratio Mathematica, No. 3, Volume 38 (2005), p. 689-701. It has recently been brought to our attention that Theorem 1 from this paper is not correct. Please note that the main conclusions of the paper do not depend at all on this theorem. However, as the authors we feel it is our responsibility to bring this erroneous theorem to your attention. As stated in the paper, Theorem 1 intends to demonstrate that there can be infinitely many elements at a given location between two sets A and B.
4
Content available remote Whitney maps-a non-metric case
100%
Charatonik J. J. , Charatonik W. J.
Colloquium Mathematicum
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2000
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tom 83
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nr 2
305-307
EN
It is shown that there is no Whitney map on the hyperspace $2^X$ for non-metrizable Hausdorff compact spaces X. Examples are presented of non-metrizable continua X which admit and ones which do not admit a Whitney map for C(X).
5
Content available remote Przestrzeń pracy pracowników warszawskich korporacji - perspektywa i kreacja przestrzeni przez dostawców wyposażenia i usług dla biur
100%
Tasarek‑Skrok K.
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2014
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nr 1(27)
281-294
EN
In my dissertation research I work on Workspace in Warsaw’s corporations. In this article I present a part of the creation of the space formed by the suppliers of equipment and services for offices. Despite my experience of cooperation with people creating office spaces, I have never focused on this phenomenon in terms of sociological issues. Ones again being a member of the Fair “Office Days”, I decided to look more closely at the proposed solutions and trends, which follow suppliers. More than once, I was surprised by the exhibitors, who proposed an unreal vision of the ideal world, free from flaws not only regarding objects but also people. I realized that the “ideal office needs perfect employee” where employee should not embarrass colleagues who belong to this space. This vision reminded me of hyperspace proposed by J. Baudrillard, where hyperreal has become more important than the true or actual reality as a result of the replacement of signs of reality.
6
Content available remote The openness of induced maps on hyperspaces
100%
Illanes A.
Colloquium Mathematicum
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1997
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tom 74
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nr 2
219-224
7
Content available remote The ANR-property of hyperspaces with the Attouch-Wets topology
100%
Voytsitskyy R.
|
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tom 6
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nr 2
228-236
EN
We characterize metric spaces whose hyperspaces of non-empty closed, bounded, compact or finite subsets, endowed with the Attouch-Wets topology, are absolute (neighborhood) retracts.
8
Content available remote The space of ANR’s in $ℝ^n$
88%
Dobrowolski T. , Rubin L. R.
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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.
9
Content available remote On the Lifshits constant for hyperspaces
75%
Leśniak K.
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2007
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tom Vol. 55, no 2
155-160
EN
The Lifshits theorem states that any k-uniformly Lipschitz map with a bounded orbit on a complete metric space X has a fixed point provided k < x(X] where x(X) is the so-called Lifshits constant of X. For many spaces we have x(X) > 1. It is interesting whether we can use the Lifshits theorem in the theory of iterated function systems. Therefore we investigate the value of the Lifshits constant for several classes of hyperspaces.
10
Content available remote On non-injectivity of Borel functions selecting points from compact sets. 2
75%
Balcerzak M. , Peredko J. , Pol R.
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2001
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tom Vol. 49, no 2
103--105
EN
The note is a supplement to (1]. We refine a result from [1] on the non-injectivity of Borel selections on the hyperspaces and we discuss the relations of the results in [1] with some results obtained by Lecomte (4].
11
Content available Hausdorff convergence of domains and their boundaries for shape optimal design
75%
Holzleitner L.
Control and Cybernetics
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2001
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tom Vol. 30, no 1
23-44
EN
A question, which arises frequently in shape optimal design, is the convergence of domains. If the objective function is defined by using the solution of a PDE with boundary conditions, then also the convergence of the boundary is of importance. In this paper a criterion for a set of domains is defined, such that from [Omega_n] --> Omega follows [Gamma_n] --> Gamma if one is restricting to this set of domains. Moreover it is proved that this criterion is sharp, meaning that if [Omega_n] --> Omega implies [Gamma_n] --> Gamma holds for any sequence of this set, then this criterion has to be fulfilled. A similar criterion for the convergence of the Lebesgue measure of the boundaries my(Gamma_n) --> my(Gamma) is given.
12
Content available remote Inducible mappings between hyperspaces
75%
Charatonik J. , Charatonik W.
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1998
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tom Vol. 46, no 1
5-9
EN
Given a continuum X we denote by [2^x] and C(X) the hyperspace of all nonempty compact subsets and of all nonempty subcontinua of X. For any two continua X and Y and a mapping [f : X --> Y let 2^f] and C(f) stand for the induced mappings between corresponding hyperspaces. A mapping g between the hypespaces is inducible is there exists a mapping f such that [g = 2^f] or g = C(f), respectively. Necessary and sufficient conditions are shown under which a given mapping g is inducible.
13
Content available remote On some forms of quasi-uniform convergence of transfinite sequence of multifunctions
75%
Przemski M.
Commentationes Mathematicae
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2010
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tom Vol. 50, [Z] 1
3-21
EN
In this paper we introduce various forms of convergence of transfinite sequences of multifunctions with values in a quasi-uniform space. We also study some weak types of continuity for such multifunctions. Any such sequence of multifunctions generates the sequence of the sets of weak types of continuity points and the sequence of various types of cluster sets of members of such sequence. We study the connection between convergence of a transfinite sequences of multifunctions and convergence of the corresponding sequences of the sets of the weak continuity points and the sequences of cluster sets. Some of the presented results concern of general nets of multifunctions.
14
Content available remote When lines go bad in hyperspace
75%
Bay C. , Lembcke A. , Schlicker S.
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tom Vol. 38, nr 3
689--701
EN
Let H(Rn) denote the hyperspace of all non-empty compact subsets of Rn. The Hausdorff metric h provides a way to measure distances between two elements of H(Rn) and generates the complete metric space (H(Rn),h)). In this paper, we examine geometric properties of lines in H(Rn), as determined by the Hausdorff metric, and compare and contrast the properties of these lines with Euclidean lines in Rn. Several surprising properties of these objects will be highlighted.
15
Content available remote Hyperspaces of Peano continua of euclidean spaces
63%
Gladdines H. , van Mill J.
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tom 142
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nr 2
173-188
EN
If X is a space then L(X) denotes the subspace of C(X) consisting of all Peano (sub)continua. We prove that for n ≥ 3 the space $L(ℝ^n)$ is homeomorphic to $B^∞$, where B denotes the pseudo-boundary of the Hilbert cube Q.
16
Content available remote The spaces of closed convex sets in Euclidean spaces with the fell topology
63%
Sakai K. , Yang Z.
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2007
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tom Vol. 55, no 2
139-143
EN
Let ConvF(Rn) be the space of all non-empty closed convex sets in Euclidean space Rn endowed with the Fell topology. We prove that ConvF(lRn) ≈ Rn x Q for every n > 1 whereas ConvF(R) ≈ R x I.
17
Content available Hyperspace retractions for curves
54%
Charatonik J. J. , Charatonik W. J. , Omiljanowski K. , Prajs J. R.
Instytut Matematyczny Polskiej Akademii Nauk
EN
CONTENTS 1. Introduction...................................5 2. Preliminaries.................................7 3. Hyperspace retractions.................9 4. Applications to selections............15 5. Applications to means.................18 References.....................................32
18
Content available remote Hereditarily weakly confluent induced mappings are homeomorphisms
51%
Charatonik J. J. , Charatonik W. J.
Colloquium Mathematicum
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1998
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tom 75
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nr 2
195-203
EN
For a given mapping f between continua we consider the induced mappings between the corresponding hyperspaces of closed subsets or of subcontinua. It is shown that if either of the two induced mappings is hereditarily weakly confluent (or hereditarily confluent, or hereditarily monotone, or atomic), then f is a homeomorphism, and consequently so are both the induced mappings. Similar results are obtained for mappings between cones over the domain and over the range continua.
19
Content available remote Probability measure functors preserving infinite-dimensional spaces
51%
Nhu N. T. , Sakai K.
Colloquium Mathematicum
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1996
|
tom 70
|
nr 2
291-304
20
Uniform properties and hyperspaces of metrizable spaces
38%
Costantini C. , Vitolo P.
Journal of Applied Analysis
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1999
|
tom Vol. 5, nr 2
187-196
EN
Two equivalent metrics can be compared, with respect to their uniform properties, in several different ways. We present some of them, and then use one of these conditions to characterize which metrics on a space induce the same lower Hausdorff topology on the hyperspace. Finally, we focus our attention to complete metrics.
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