A class of arcwise connected continua

Author:
Charles L. Hagopian

Journal:
Proc. Amer. Math. Soc. **30** (1971), 164-168

MSC:
Primary 54.55

DOI:
https://doi.org/10.1090/S0002-9939-1971-0281164-1

MathSciNet review:
0281164

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Abstract | References | Similar Articles | Additional Information

Abstract: It is known that every bounded semi-aposyndetic plane continuum which does not separate the plane is arcwise connected. To show that this theorem remains true if the phrase ``does not separate the plane'' is replaced by ``does not have infinitely many complementary domains'' is the primary purpose of this paper.

**[1]**C. L. Hagopian,*Concerning the cyclic connectivity of plane continua*, Michigan Math. J. (to appear). MR**0300248 (45:9294)****[2]**-,*Semiaposyndetic nonseparating plane continua are arcwise connected*, Bull. Amer. Math. Soc.**77**(1971), 593-595. MR**0283774 (44:1004)****[3]**-,*An arc theorem for plane continua*, Illinois J. Math. (to appear). MR**0314010 (47:2562)****[4]**F. B. Jones,*Aposyndetic continua and certain boundary problems*, Amer. J. Math.**63**(1941), 545-553. MR**3**, 59. MR**0004771 (3:59e)****[5]**-,*The cyclic connectivity of plane continua*, Pacific J. Math.**11**(1961), 1013-1016. MR**25**#2583. MR**0139145 (25:2583)****[6]**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**0150722 (27:709)****[7]**G. T. Whyburn,*Analytic topology*, Amer. Math. Soc. Colloq. Publ., vol. 28, Amer. Math. Soc., Providence, R. I., 1963. MR**32**#425. MR**0182943 (32:425)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1971-0281164-1

Keywords:
Arcwise connected continua,
aposyndesis,
semi-aposyndesis,
cut point,
complementary domain,
Jones's cyclic property

Article copyright:
© Copyright 1971
American Mathematical Society