Some generalisations of the Scherrar Fixed-Point Theorem

W. Ayres

Displaying similar documents to “Some generalisations of the Scherrar Fixed-Point Theorem”

Size levels for arcs

Sam Nadler, T. West (1992)

Fundamenta Mathematicae

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We determine the size levels for any function on the hyperspace of an arc as follows. Assume Z is a continuum and consider the following three conditions: 1) Z is a planar AR; 2) cut points of Z have component number two; 3) any true cyclic element of Z contains at most two cut points of Z. Then any size level for an arc satisfies 1)-3) and conversely, if Z satisfies 1)-3), then Z is a diameter level for some arc.

Some theorems on the embeddability of ANR-spaces into Euclidean spaces

Hanna Patkowska (1969)

Fundamenta Mathematicae

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Finite arc-sums

Norman Steenrod (1934)

Fundamenta Mathematicae

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Some theorems about the embeddability of ANR-sets into decomposition spaces of $E^{n}$

Hanna Patkowska (1971)

Fundamenta Mathematicae

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Decompositions of cyclic elements of locally connected continua

D. Daniel (2010)

Colloquium Mathematicae

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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.