Glasnik matematički, Vol. 48 No. 1, 2013.
Original scientific paper
https://doi.org/10.3336/gm.48.1.13
Continuum-chainable continuum which can not be mapped onto an arcwise connected continuum by a monotone epsilon mapping
Pavel Pyrih
; Faculty of Mathematics and Physics, Charles University in Prague, 118 00 Prague, Czech Republic
Benjamin Vejnar
orcid.org/0000-0002-2833-5385
; Faculty of Mathematics and Physics, Charles University in Prague, 118 00 Prague, Czech Republic
Luis Miguel García Velázquez
; Universidad Nacional Autónoma de México, Mexico City, D. F., Mexico
Abstract
A continuum is called continuum-chainable provided for any pair of points and positive epsilon there exists a finite weak chain of subcontinua of diameter less than epsilon starting at one point and ending in the other. We present an example of a continuum which is continuum-chainable and which can not be mapped onto an arcwise connected continuum by a monotone epsilon mapping. This answers a question posed by W. J. Charatonik.
Keywords
Continuum; continuum-chainable; monotone mapping; arcwise connected
Hrčak ID:
103353
URI
Publication date:
4.6.2013.
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