Glasnik Matematicki, Vol. 51, No. 1 (2016), 237-253.

NON-CUT, SHORE AND NON-BLOCK POINTS IN CONTINUA

Jozef Bobok, Pavel Pyrih and Benjamin Vejnar

Faculty of Mathematics and Physics, Charles University in Prague, 118 00 Prague, Czech Republic

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

Abstract.   In a nondegenerate continuum we study the set of non-cut points. We show that it can be stratified by inclusion into six natural subsets (containing also non-block and shore points). Among other results we show that every nondegenerate continuum contains at least two non-block points. Our investigation is further focused on both the classes of arc-like and circle-like continua.

2010 Mathematics Subject Classification.   54F15, 54D10.

Key words and phrases.   Continuum, shore point, non-cut point, arc-like continuum.

DOI: 10.3336/gm.51.1.14

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