On complete metric spaces containing the Sierpinski curve
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- by Janusz R. Prajs PDF
- Proc. Amer. Math. Soc. 126 (1998), 3743-3747 Request permission
Abstract:
It is proved that a complete metric space topologically contains the Sierpiński universal plane curve if and only if it has a subset with so-called bypass property, i.e. it has a subset $K$ containing an arc such that for each $a\in K$ and for each open arc $A\subset K$ with $a\in A$, there exists an arbitrary small arc in $K\setminus \{a\}$ joining the two components of $A\setminus \{a\}$.References
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Additional Information
- Janusz R. Prajs
- Affiliation: Institute of Mathematics, Opole University, ul. Oleska 48, 45-052 Opole, Poland
- Email: jrprajs@math.uni.opole.pl
- Received by editor(s): December 19, 1996
- Received by editor(s) in revised form: April 21, 1997
- Additional Notes: The author expresses grateful thanks to Prof. K. Omiljanowski for his help in the preparation of this paper.
- Communicated by: Alan Dow
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 3743-3747
- MSC (1991): Primary 54F15, 54F65, 54F50, 54C25
- DOI: https://doi.org/10.1090/S0002-9939-98-04509-2
- MathSciNet review: 1458258