On uncountable collections of continua and their span

Repovš, Dušan ; Skopenkov, Arkadij ; Ščepin, Evgenij

Colloquium Mathematicae, Tome 70 (1996), p. 289-296 / Harvested from The Polish Digital Mathematics Library

Résumé

We prove that if the Euclidean plane $ℝ^2$ 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 $X ⊂ ℝ^2$ 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.

Détail

Publié le : 1996-01-01

Zbl 0882.54030

EUDML-ID : urn:eudml:doc:210342

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