On complete metric spaces containing the Sierpinski curve
Author:
Janusz R. Prajs
Journal:
Proc. Amer. Math. Soc. 126 (1998), 37433747
MSC (1991):
Primary 54F15, 54F65, 54F50, 54C25
MathSciNet review:
1458258
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Abstract: It is proved that a complete metric space topologically contains the Sierpinski universal plane curve if and only if it has a subset with socalled bypass property, i.e. it has a subset containing an arc such that for each and for each open arc with , there exists an arbitrary small arc in joining the two components of .
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Additional Information
Janusz R. Prajs
Affiliation:
Institute of Mathematics, Opole University, ul. Oleska 48, 45052 Opole, Poland
Email:
jrprajs@math.uni.opole.pl
DOI:
http://dx.doi.org/10.1090/S0002993998045092
PII:
S 00029939(98)045092
Keywords:
Bypass property,
embedding,
homogeneity,
local separating point,
Sierpi\'nski curve
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
Article copyright:
© Copyright 1998
American Mathematical Society
