Displaying similar documents to “Locally connected exceptional minimal sets of surface homeomorphisms”

Closed connected sets which remain connected upon the removal of certain, connected subsets

John Kline (1924)

Fundamenta Mathematicae

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The purpose of this paper is to prove: Theorem: Suppose M is a closed connected set containing more than one point such that if g is any connected subset of M, then M-g is connected. Under these conditions M is a simple closed curve. Theorem: If M is an unbounded closed connected set which remains connected upon the removal of any unbounded connected proper subset, then M is either an open curve, a ray of an open curve or a simple closed curve J plus OP, a ray of an open curve which...

Removing sets from connected product spaces while preserving connectedness

Melvin Henriksen, Amir Nikou (2007)

Commentationes Mathematicae Universitatis Carolinae

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As per the title, the nature of sets that can be removed from a product of more than one connected, arcwise connected, or point arcwise connected spaces while preserving the appropriate kind of connectedness is studied. This can depend on the cardinality of the set being removed or sometimes just on the cardinality of what is removed from one or two factor spaces. Sometimes it can depend on topological properties of the set being removed or its trace on various factor spaces. Some of...