Glasnik Matematicki, Vol. 55, No. 2 (2020), 375-375.

ERRATA TO ``NON-CUT, SHORE AND NON-BLOCK POINTS IN CONTINUA"

Jozef Bobok, Pavel Pyrih and Benjamin Vejnar

Faculty of Civil Engineering, Czech Technical University in Prague, Czech Republic

Faculty of Mathematics and Physics, Charles University in Prague, Czech Republic

Faculty of Mathematics and Physics, Charles University in Prague, 118 00 Prague, Czech Republic
e-mail: vejnar@karlin.mff.cuni.cz


The aim of this errata is to claim that [2, Theorem 4.5] is not true. This mistake was pointed to us by W. J. Charatonik. In the false "proof" of [2, Theorem 4.5] the authors argue by a false note mentioned by Bing that every continuum which is both arc-like and circle-like is indecomposable [1, p. 121]. A counterexample to Bing's note as well as to [2, Theorem 4.5] is given by two bucket-handle continua joined by their end-points. Another counterexample is described in [3, Examples].


Full text (PDF) (free access)

https://doi.org/10.3336/gm.55.2.13


References:

  1. R. H. Bing, Embedding circle-like continua in the plane, Canadian J. Math. 14 (1962), 113-128.
    MathSciNet     CrossRef

  2. J. Bobok, P. Pyrih and B. Vejnar, Non-cut, shore and non-block points in continua, Glas. Mat. Ser. III 51(71) (2016), 237-253.
    MathSciNet     CrossRef

  3. C. E. Burgess, Chainable continua and indecomposability, Pacific J. Math. 9 (1959), 653-659.
    MathSciNet     CrossRef

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