Sets accessible at each point only by wild arcs

Author:
Gary Glenn Miller

Journal:
Proc. Amer. Math. Soc. **31** (1972), 583-590

DOI:
https://doi.org/10.1090/S0002-9939-1972-0284992-2

MathSciNet review:
0284992

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Abstract | References | Additional Information

Abstract: A positional pathology as described in the title is shown to occur in three-space. We construct an arcwise accessible point set such that each arc to is locally knotted at uncountably many points. In addition we give examples of connected, locally connected point sets and which are accessible at each point only by wild arcs and tame arcs respectively. The point set has countably many components, and each of these is a tame finite -complex. Moreover is locally connected and arcwise connected.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1972-0284992-2

Keywords:
Arcwise accessible,
wild arc,
tame -complex,
arcwise connected,
locally connected,
dense subset of

Article copyright:
© Copyright 1972
American Mathematical Society