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ArticleOriginal scientific text

Title

On uncountable collections of continua and their span

Authors 1, 2, 3

Affiliations

  1. University of Trieste, 1, Piazzale Europa, 34100 Trieste, Italy
  2. Faculty of Mechanics And Mathematics, Moscow State University, Vorobyovy Hills, 117899 Moscow, Russia
  3. Steklov Mathematical Institute, Russian Academy of Sciences, 42, Vavilova Street, 117966 Moscow, Russia

Abstract

We prove that if the Euclidean plane ℝ2 contains an uncountable collection of pairwise disjoint copies of a tree-like continuum X, then the symmetric span of X is zero, sX = 0. We also construct a modification of the Oversteegen-Tymchatyn example: for each ε > 0 there exists a tree X⊂ℝ2 such that σX < ε but X cannot be covered by any 1-chain. These are partial solutions of some well-known problems in continua theory.

Keywords

ENG
uncountable collection of compacta, deleted product, chainable continua, span, equivariant maps, symmetric span

Bibliography

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Colloquium Mathematicum
1996/69/2
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Pages:
289-296
Main language of publication
English
Received
1993-10-06
Accepted
1995-02-21
Published
1996
Exact and natural sciences