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Decompositions of cyclic elements of locally connected continua

100%

Daniel D.

Colloquium Mathematicum

2010

tom 119

nr 2

321-330

Let X denote a locally connected continuum such that cyclic elements have metrizable $G_{δ}$ boundary in X. We study the cyclic elements of X by demonstrating that each such continuum gives rise to an upper semicontinuous decomposition G of X into continua such that X/G is the continuous image of an arc and the cyclic elements of X correspond to the cyclic elements of X/G that are Peano continua.

Non-separating subcontinua of planar continua

51%

Daniel D., Islas C., Leonel R., Tymchatyn E.

Colloquium Mathematicum

2015

tom 141

nr 1

143-148

We revisit an old question of Knaster by demonstrating that each non-degenerate plane hereditarily unicoherent continuum X contains a proper, non-degenerate subcontinuum which does not separate X.

Ograniczanie wyników

2 Colloquium Mathematicum

2 Daniel D.

1 Islas C.

1 Leonel R.

1 Tymchatyn E.

1 2015

1 2010

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Decompositions of cyclic elements of locally connected continua

Non-separating subcontinua of planar continua