A class of arcwise connected continua

Author:
Charles L. Hagopian

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

MSC:
Primary 54.55

MathSciNet review:
0281164

Full-text PDF Free Access

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]**Charles L. Hagopian,*The cyclic connectivity of plane continua*, Michigan Math. J.**18**(1971), 401–407. MR**0300248****[2]**Charles L. Hagopian,*Semiaposyndetic nonseparating plane continua are arcwise connected.*, Bull. Amer. Math. Soc.**77**(1971), 593–595. MR**0283774**, 10.1090/S0002-9904-1971-12765-9**[3]**Charles L. Hagopian,*An arc theorem for plane continua*, Illinois J. Math.**17**(1973), 82–89. MR**0314010****[4]**F. Burton Jones,*Aposyndetic continua and certain boundary problems*, Amer. J. Math.**63**(1941), 545–553. MR**0004771****[5]**F. Burton Jones,*The cyclic connectivity of plane continua*, Pacific J. Math.**11**(1961), 1013–1016. MR**0139145****[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, Vol. XXVIII, American Mathematical Society, Providence, R.I., 1963. MR**0182943**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
54.55

Retrieve articles in all journals with MSC: 54.55

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