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On uncountable collections of continua and their span

Dušan Repovš, Arkadij Skopenkov, Evgenij Ščepin (1996)

Colloquium Mathematicae

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 $X \subset ℝ^{2}$ 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.

On uniquely arcwise connected curves

Roman Mańka (1987)

Colloquium Mathematicae

On universality of finite powers of locally path-connected meager spaces

Taras Banakh, Robert Cauty (2005)

Colloquium Mathematicae

It is shown that for every integer n the (2n+1)th power of any locally path-connected metrizable space of the first Baire category is 𝓐₁[n]-universal, i.e., contains a closed topological copy of each at most n-dimensional metrizable σ-compact space. Also a one-dimensional σ-compact absolute retract X is found such that the power X^{n+1} is 𝓐₁[n]-universal for every n.

Displaying 41 – 46 of 46

On uncountable collections of continua and their span

On uniquely arcwise connected curves

On universality of finite powers of locally path-connected meager spaces

On weakly zero-dimensional mappings

One dimensional locally setwise homogeneous continua

Ordering the local subsemigroups of a semigroup.

Currently displaying 41 – 46 of 46