A note on Jones' function

Author:
John Rosasco

Journal:
Proc. Amer. Math. Soc. **49** (1975), 501-504

MSC:
Primary 54F20

DOI:
https://doi.org/10.1090/S0002-9939-1975-0367946-X

MathSciNet review:
0367946

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Abstract | References | Similar Articles | Additional Information

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.

**[1]**Charles L. Hagopian,*A cut point theorem for plane continua*, Duke Math. J.**38**(1971), 509–512. MR**0284980****[2]**Charles L. Hagopian,*Arcwise connectivity of semi-aposyndetic plane continua*, Pacific J. Math.**37**(1971), 683–686. MR**0307202****[3]**-,*Concerning Jones's function*, Notices Amer. Math. Soc.**19**(1972), A-779. Abstract #698-G2.**[4]**F. Burton Jones,*A characterization of a semi-locally-connected plane continuum*, Bull. Amer. Math. Soc.**53**(1947), 170–175. MR**0019301**, https://doi.org/10.1090/S0002-9904-1947-08776-0**[5]**F. Burton Jones,*Concerning non-aposyndetic continua*, Amer. J. Math.**70**(1948), 403–413. MR**0025161**, https://doi.org/10.2307/2372339**[6]**R. L. Moore,*Foundations of point set theory*, Revised edition. American Mathematical Society Colloquium Publications, Vol. XIII, American Mathematical Society, Providence, R.I., 1962. MR**0150722****[7]**Gordon Thomas Whyburn,*Analytic Topology*, American Mathematical Society Colloquium Publications, v. 28, American Mathematical Society, New York, 1942. MR**0007095**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1975-0367946-X

Keywords:
Jones' function ,
aposyndesis,
folded complementary domain,
nonlocally connected plane continua

Article copyright:
© Copyright 1975
American Mathematical Society