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Continua which admit no mean

100%

Kawamura K., Tymchatyn E. D.

Colloquium Mathematicum

1996

tom 71

nr 1

97-105

A symmetric, idempotent, continuous binary operation on a space is called a mean. In this paper, we provide a criterion for the non-existence of mean on a certain class of continua which includes tree-like continua. This generalizes a result of Bell and Watson. We also prove that any hereditarily indecomposable circle-like continuum admits no mean.

Hereditarily indecomposable inverse limits of graphs

81%

Kawamura K., Tuncali H., Tymchatyn E.

Fundamenta Mathematicae

2005

tom 185

nr 3

195-210

We prove the following theorem: Let G be a compact connected graph and let f: G → G be a piecewise linear surjection which satisfies the following condition: for each nondegenerate subcontinuum A of G, there is a positive integer n such that fⁿ(A) = G. Then, for each ε > 0, there is a map $f_{ε}: G → G$ which is ε-close to f such that the inverse limit $(G,f_{ε})$ is hereditarily indecomposable.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Fundamenta Mathematicae

2 Kawamura K.

1 Tuncali H.

1 Tymchatyn E.

1 Tymchatyn E. D.

1 2005

1 1996

Wyniki wyszukiwania

Continua which admit no mean

Hereditarily indecomposable inverse limits of graphs