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 ) was established in  for and in  in complete generality. Cf. Weight of a topological space.
|||P.S. Aleksandrov, P. Urysohn, "Mémoire sur les espaces topologiques compacts" , Koninkl. Nederl. Akad. Wetensch. , Amsterdam (1929)|
|||R. Engelking, "General topology" , PWN (1977) (Translated from Polish)|
|||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)|
|||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)|
|||A.V. Arkhangel'skii, V.I. Ponomarev, "Fundamentals of general topology: problems and exercises" , Reidel (1984) (Translated from Russian)|
Addition theorem. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Addition_theorem&oldid=11896