A note on Jones' function
Author:
John Rosasco
Journal:
Proc. Amer. Math. Soc. 49 (1975), 501504
MSC:
Primary 54F20
MathSciNet review:
0367946
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Abstract: For each point of a continuum , F. B. Jones [5, Theorem 2] defines to be the closed set consisting of all points of such that is not aposyndetic at with respect to . Suppose is a plane continuum and for any positive real number there are at most a finite number of complementary domains of of diameter greater than . In this paper it is proved that for each point of , the set is connected.
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 , Concerning nonaposyndetic continua, Amer. J. Math. 70 (1948), 403413. MR 9, 606. MR 0025161 (9:606h)
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 R. L. Moore, Foundations of point set theory, rev. ed., Amer. Math. Soc. Colloq. Publ., vol. 13, Amer. Math. Soc., Providence, R. I., 1962. MR 27 #709. MR 0150722 (27:709)
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 G. T. Whyburn, Analytic topology, Amer. Math. Soc. Colloq. Publ., vol. 28, Amer. Math. Soc., Providence, R. I., 1942. MR 4, 86. MR 0007095 (4:86b)
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DOI:
http://dx.doi.org/10.1090/S0002993919750367946X
PII:
S 00029939(1975)0367946X
Keywords:
Jones' function ,
aposyndesis,
folded complementary domain,
nonlocally connected plane continua
Article copyright:
© Copyright 1975 American Mathematical Society
