Arcwise connectedness of semiaposyndetic plane continua
HTML articles powered by AMS MathViewer
- by Charles L. Hagopian
- Trans. Amer. Math. Soc. 158 (1971), 161-165
- DOI: https://doi.org/10.1090/S0002-9947-1971-0284981-1
- PDF | Request permission
Abstract:
In a recent paper, the author proved that if a compact plane continuum $M$ contains a finite point set $F$ such that, for each point $x$ in $M - F,M$ is semi-locally-connected and not aposyndetic at $x$, then $M$ 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.References
- 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 254823, DOI 10.1090/S0002-9947-1970-0254823-8
- Charles L. Hagopian, A cut point theorem for plane continua, Duke Math. J. 38 (1971), 509–512. MR 284980
- Charles L. Hagopian, The cyclic connectivity of plane continua, Michigan Math. J. 18 (1971), 401–407. MR 300248
- F. Burton Jones, Aposyndetic continua and certain boundary problems, Amer. J. Math. 63 (1941), 545–553. MR 4771, DOI 10.2307/2371367
- F. Burton Jones, A characterization of a semi-locally-connected plane continuum, Bull. Amer. Math. Soc. 53 (1947), 170–175. MR 19301, DOI 10.1090/S0002-9904-1947-08776-0
- F. Burton Jones, Concerning non-aposyndetic continua, Amer. J. Math. 70 (1948), 403–413. MR 25161, DOI 10.2307/2372339 —, Problems in the plane, Summary of Lectures and Seminars, Summer Institute on Set Theoretic Topology, Madison, Wisconsin 1955; revised 1957, pp. 70-71.
- 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
- G. T. Whyburn, Semi-locally connected sets, Amer. J. Math. 61 (1939), 733–749. MR 182, DOI 10.2307/2371330 —, Analytic topology, rev. ed., Amer. Math. Soc. Colloq. Publ., vol. 28, Amer. Math. Soc., Providence, R. I., 1963. MR 32 #425.
Bibliographic Information
- © Copyright 1971 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 158 (1971), 161-165
- MSC: Primary 54.55
- DOI: https://doi.org/10.1090/S0002-9947-1971-0284981-1
- MathSciNet review: 0284981