Compact sets definable by free $3$-manifolds
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- by W. H. Row PDF
- Trans. Amer. Math. Soc. 197 (1974), 225-244 Request permission
Abstract:
Shape conditions are given that force a compactum (i.e., a compact metric space) embedded in the interior of a nonclosed, piecewise-linear 3-manifold to have arbitrarily close, compact, polyhedral neighborhoods each component of which is a 3-manifold with free fundamental group (i.e., to be definable by free 3-manifolds). For compact, connected ANR’s these conditions reduce to the criterion of having a free fundamental group. Additional conditions are given that insure definability by handlebodies or cubes-with-handles. An embedding of Menger’s universal 1-dimensional curve in Euclidean 3-space is shown to have the property that all tame surfaces, separating in 3-space a fixed pair of points, cannot be adjusted (by a small space homeomorphism) to intersect the embedded curve in a 0-dimensional set.References
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Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 197 (1974), 225-244
- MSC: Primary 57A10; Secondary 54C56
- DOI: https://doi.org/10.1090/S0002-9947-1974-0362314-2
- MathSciNet review: 0362314