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On uncountable collections of continua and their span

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Repovš D., Skopenkov A. B., Ščepin E. V.

Colloquium Mathematicum

1996

tom 69

nr 2

289-296

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.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Repovš D.

1 Skopenkov A. B.

1 Ščepin E. V.

1 1996

Wyniki wyszukiwania

On uncountable collections of continua and their span