Arcwise connectedness of semiaposyndetic plane continua

Author:
Charles L. Hagopian

Journal:
Trans. Amer. Math. Soc. **158** (1971), 161-165

MSC:
Primary 54.55

MathSciNet review:
0284981

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In a recent paper, the author proved that if a compact plane continuum contains a finite point set such that, for each point in is semi-locally-connected and not aposyndetic at , then is arcwise connected. The primary purpose of this paper is to generalize that theorem. Semiaposyndesis, a generalization of semi-local-connectedness, is defined and arcwise connectedness is established for certain semiaposyndetic plane continua.

**[1]**Charles L. Hagopian,*Concerning arcwise connectedness and the existence of simple closed curves in plane continua*, Trans. Amer. Math. Soc.**147**(1970), 389–402. MR**0254823**, 10.1090/S0002-9947-1970-0254823-8**[2]**Charles L. Hagopian,*A cut point theorem for plane continua*, Duke Math. J.**38**(1971), 509–512. MR**0284980****[3]**Charles L. Hagopian,*The cyclic connectivity of plane continua*, Michigan Math. J.**18**(1971), 401–407. MR**0300248****[4]**F. Burton Jones,*Aposyndetic continua and certain boundary problems*, Amer. J. Math.**63**(1941), 545–553. MR**0004771****[5]**F. Burton Jones,*A characterization of a semi-locally-connected plane continuum*, Bull. Amer. Math. Soc.**53**(1947), 170–175. MR**0019301**, 10.1090/S0002-9904-1947-08776-0**[6]**F. Burton Jones,*Concerning non-aposyndetic continua*, Amer. J. Math.**70**(1948), 403–413. MR**0025161****[7]**-,*Problems in the plane*, Summary of Lectures and Seminars, Summer Institute on Set Theoretic Topology, Madison, Wisconsin 1955; revised 1957, pp. 70-71.**[8]**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****[9]**G. T. Whyburn,*Semi-locally connected sets*, Amer. J. Math.**61**(1939), 733–749. MR**0000182****[10]**-,*Analytic topology*, rev. ed., Amer. Math. Soc. Colloq. Publ., vol. 28, Amer. Math. Soc., Providence, R. I., 1963. MR**32**#425.

Retrieve articles in *Transactions 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/S0002-9947-1971-0284981-1

Keywords:
Semiaposyndesis,
semi-local-connectedness,
aposyndesis,
arcwise connected continua,
folded complementary domain

Article copyright:
© Copyright 1971
American Mathematical Society