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Smooth continuum

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at a point

A continuum such that for each sequence of points of converging towards a point and each subcontinuum containing and there exist a sequence of subcontinua in , , converging towards . A continuum that is smooth at each one of its points is called smooth.


Comments

Smoothness has a slightly different definition in the class of uniquely arcwise-connected continua, or dendroids (a continuum is uniquely arcwise-connected if for every and in there is a unique arc in connecting and ). One calls a uniquely arcwise-connected continuum smooth if there is a such that whenever in . Such a point is called an initial point of .

References

[a1] J.J. Charatonik, C. Eberhart, "On smooth dendroids" Fund. Math. , 67 (1970) pp. 297–322
How to Cite This Entry:
Smooth continuum. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Smooth_continuum&oldid=31974
This article was adapted from an original article by A.A. Mal'tsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article