# On uncountable collections of continua and their span

Dušan Repovš; Arkadij Skopenkov; Evgenij Ščepin

Colloquium Mathematicae (1996)

- Volume: 69, Issue: 2, page 289-296
- ISSN: 0010-1354

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topRepovš, Dušan, Skopenkov, Arkadij, and Ščepin, Evgenij. "On uncountable collections of continua and their span." Colloquium Mathematicae 69.2 (1996): 289-296. <http://eudml.org/doc/210342>.

@article{Repovš1996,

abstract = {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.},

author = {Repovš, Dušan, Skopenkov, Arkadij, Ščepin, Evgenij},

journal = {Colloquium Mathematicae},

keywords = {uncountable collection of compacta; deleted product; chainable continua; span; equivariant maps; symmetric span; tree-like continuum},

language = {eng},

number = {2},

pages = {289-296},

title = {On uncountable collections of continua and their span},

url = {http://eudml.org/doc/210342},

volume = {69},

year = {1996},

}

TY - JOUR

AU - Repovš, Dušan

AU - Skopenkov, Arkadij

AU - Ščepin, Evgenij

TI - On uncountable collections of continua and their span

JO - Colloquium Mathematicae

PY - 1996

VL - 69

IS - 2

SP - 289

EP - 296

AB - 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.

LA - eng

KW - uncountable collection of compacta; deleted product; chainable continua; span; equivariant maps; symmetric span; tree-like continuum

UR - http://eudml.org/doc/210342

ER -

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