Addition theorem
From Encyclopedia of Mathematics
for weights
If a Hausdorff compactum 
can be represented as the union over a set of infinite cardinality 
of its subspaces of weight 
, then the weight of 
does not exceed 
. The addition theorem (which was formulated as a problem in [1]) was established in [3] for 
and in [4] in complete generality. Cf. Weight of a topological space.
References
| [1] | P.S. Aleksandrov, P. Urysohn, "Mémoire sur les espaces topologiques compacts" , Koninkl. Nederl. Akad. Wetensch. , Amsterdam (1929) |
| [2] | R. Engelking, "General topology" , PWN (1977) (Translated from Polish) |
| [3] | Yu.M. Smirnov, "On metrizability of bicompacta, decomposable as a sum of sets with a countable base" Fund. Math. , 43 (1956) pp. 387–393 (In Russian) |
| [4] | A.V. Arkhangel'skii, "An addition theorem for weights of sets lying in bicompacta" Dokl. Akad. Nauk SSSR , 126 : 2 (1959) pp. 239–241 (In Russian) |
| [5] | A.V. Arkhangel'skii, V.I. Ponomarev, "Fundamentals of general topology: problems and exercises" , Reidel (1984) (Translated from Russian) |
How to Cite This Entry:
Addition theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Addition_theorem&oldid=26133
Addition theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Addition_theorem&oldid=26133
This article was adapted from an original article by A.V. Arkhangel'skii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article