A sufficient condition for countable-set aposyndesis
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- by Donald E. Bennett PDF
- Proc. Amer. Math. Soc. 32 (1972), 578-584 Request permission
Abstract:
In this paper a stronger form of aposyndesis is defined and continua with this property (strongly aposyndetic) are shown to be countable-set aposyndetic. Although every continuum which is a product of nondegenerate continua is countable-set aposyndetic, it is established that no product of nondegenerate continua is strongly aposyndetic.References
- Donald E. Bennett, Aposyndetic properties of unicoherent continua, Pacific J. Math. 37 (1971), 585–589. MR 305370
- R. W. FitzGerald, The cartesian product of non-degenerate compact continua is $n$-point aposyndetic, Topology Conference (Arizona State Univ., Tempe, Ariz., 1967) Arizona State Univ., Tempe, Ariz., 1968, pp. 324–326. MR 0236861
- F. Burton Jones, Aposyndetic continua and certain boundary problems, Amer. J. Math. 63 (1941), 545–553. MR 4771, DOI 10.2307/2371367
- Casimir Kuratowski, Topologie. Vol. II, Monografie Matematyczne, Tom 21, Państwowe Wydawnictwo Naukowe, Warsaw, 1961 (French). Troisième édition, corrigèe et complétée de deux appendices. MR 0133124 S. Mazurkiewicz, Sur l’existence des continus indécomposables, Fund. Math. 25 (1935), 327-328.
- Eldon Jon Vought, A classification scheme and characterization of certain curves, Colloq. Math. 20 (1969), 91–98. MR 238274, DOI 10.4064/cm-20-1-91-98
- Eldon Jon Vought, $n$-aposyndetic continua and cutting theorems, Trans. Amer. Math. Soc. 140 (1969), 127–135. MR 242128, DOI 10.1090/S0002-9947-1969-0242128-2
- G. T. Whyburn, Semi-locally connected sets, Amer. J. Math. 61 (1939), 733–749. MR 182, DOI 10.2307/2371330 —, Analytical topology, Amer. Math. Soc. Colloq. Publ., vol. 28, Amer. Math. Soc., Providence, R.I., 1942. MR 4, 86.
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 32 (1972), 578-584
- MSC: Primary 54F15
- DOI: https://doi.org/10.1090/S0002-9939-1972-0293594-3
- MathSciNet review: 0293594