Smooth continuum
From Encyclopedia of Mathematics
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
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