Displaying similar documents to “On hereditarily indecomposable compacta”

Factorwise rigidity of embeddings of products of pseudo-arcs

Mauricio E. Chacón-Tirado, Alejandro Illanes, Rocío Leonel (2012)

Colloquium Mathematicae

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An embedding from a Cartesian product of two spaces into the Cartesian product of two spaces is said to be factorwise rigid provided that it is the product of embeddings on the individual factors composed with a permutation of the coordinates. We prove that each embedding of a product of two pseudo-arcs into itself is factorwise rigid. As a consequence, if X and Y are metric continua with the property that each of their nondegenerate proper subcontinua is homeomorphic to the pseudo-arc,...

Pseudo-homotopies of the pseudo-arc

Alejandro Illanes (2012)

Commentationes Mathematicae Universitatis Carolinae

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Let X be a continuum. Two maps g , h : X → X are said to be pseudo-homotopic provided that there exist a continuum C , points s , t ∈ C and a continuous function H : X × C → X such that for each x ∈ X , H ( x , s ) = g ( x ) and H ( x , t ) = h ( x ) . In this paper we prove that if P is the pseudo-arc, g is one-to-one and h is pseudo-homotopic to g , then g = h . This theorem generalizes previous results by W. Lewis and M. Sobolewski.

Continua which admit no mean

K. Kawamura, E. Tymchatyn (1996)

Colloquium Mathematicae

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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.