Generalized Cantor manifolds and indecomposable continua

Todorov, Vladimir; Valov, Vesko

doi:10.48550/arxiv.1204.2873

2012

DOI: 10.48550/arxiv.1204.2873

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Generalized Cantor manifolds and indecomposable continua

Vladimir Todorov¹,

Vesko Valov²

Abstract: We review results concerning homogeneous compacta and discuss some open questions. It is established that indecomposable continua are Alexandroff (resp., Mazurkiewicz, or strong Cantor) manifolds with respect to the class of all continua. We also provide some new proofs of Bing's theorems about separating metric compacta by hereditarily indecomposable compacta.

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2014

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Alexandroff Manifolds and Homogeneous Continua

Karassev¹,

Todorov²,

Valov³

2014

Can. math. bull.

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Abstract. We prove the following result of the second and third authors: Any ho-where G is a principal ideal domain. This implies that any homogeneous n-dimensional metric ANR-continuum is a V n -continuum in the sense of Alexandroff.We also prove that any finite-dimensional homogeneous metric continuum X, satisfyingȞ n (X; G) = 0 for some group G and n ≥ 1, cannot be separated by a compactum K withȞ n−1 (K; G) = 0 and dim G K ≤ n − 1. This provides a partial answer to a question of Kallipoliti-Papasoglu whether any two-dimensional homogeneous Peano continuum cannot be separated by arcs.

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Alexandroff Manifolds and Homogeneous Continua

Karassev¹,

Todorov²,

Valov³

2014

Can. math. bull.

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Generalized Cantor manifolds and indecomposable continua

Cited by 1 publication

References 14 publications

Alexandroff Manifolds and Homogeneous Continua

Alexandroff Manifolds and Homogeneous Continua

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