Addition theorem
From Encyclopedia of Mathematics
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.
for weights
If a Hausdorff compactum $X$ can be represented as the union over a set of infinite cardinality $\leq\tau$ of its subspaces of weight $\leq\tau$, then the weight of $X$ does not exceed $\tau$. The addition theorem (which was formulated as a problem in [AlUr]) was established in [Sm] for $\tau=\aleph_0$ and in [Ar] in complete generality. Cf. Weight of a topological space.
References
[AlUr] | P.S. Aleksandrov, P. Urysohn, "Mémoire sur les espaces topologiques compacts", Koninkl. Nederl. Akad. Wetensch., Amsterdam (1929) |
[Ar] | 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) |
[ArPo] | A.V. Arkhangel'skii, V.I. Ponomarev, "Fundamentals of general topology: problems and exercises", Reidel (1984) (Translated from Russian) |
[En] | R. Engelking, "General topology", PWN (1977) (Translated from Polish) |
[Sm] | 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) |
How to Cite This Entry:
Addition theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Addition_theorem&oldid=26134
Addition theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Addition_theorem&oldid=26134
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