A nonshrinkable decomposition of whose nondegenerate elements are contained in a cellular arc

Authors:
W. H. Row and John J. Walsh

Journal:
Trans. Amer. Math. Soc. **289** (1985), 227-252

MSC:
Primary 57N10; Secondary 54B10, 57N30, 57N60

DOI:
https://doi.org/10.1090/S0002-9947-1985-0779062-4

MathSciNet review:
779062

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Abstract | References | Similar Articles | Additional Information

Abstract: A decomposition of is constructed with the following properties:

(1) The set of all nondegenerate elements consists of a null sequence of arcs and is a simple closed curve.

(2) Each arc contained in is cellular.

(3) is the boundary of a disk that is locally flat except at points of .

(4) The decomposition is not shrinkable; that is, the decomposition space is not homeomorphic to .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1985-0779062-4

Keywords:
Cellular decomposition,
cellular arc,
nonshrinkable,
-manifold

Article copyright:
© Copyright 1985
American Mathematical Society