Geodesic
On uncountable collections of continua and their span
Colloquium Mathematicum, Tome 69 (1996) no. 2, pp. 289-296 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm-69-2-289-296
Keywords: uncountable collection of compacta, deleted product, chainable continua, span, equivariant maps, symmetric span

Dušan Repovš 1 ; Arkadij Skopenkov 1 ; Evgenij Ščepin 1

1 
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Dušan Repovš; Arkadij Skopenkov; Evgenij Ščepin. On uncountable collections of continua and their span. Colloquium Mathematicum, Tome 69 (1996) no. 2, pp. 289-296. doi: 10.4064/cm-69-2-289-296

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