Dyadic space

For another use, see Dyadic space (cell biology).

In mathematics, a dyadic compactum is a Hausdorff topological space that is the continuous image of a product of discrete two-point spaces,[1] and a dyadic space is a topological space with a compactification which is a dyadic compactum.[2] However, many authors use the term dyadic space with the same meaning as dyadic compactum above.[3][4][5]

Dyadic compacta and spaces satisfy the Suslin condition, and were introduced by Russian mathematician Pavel Alexandrov.[1] Polyadic spaces are generalisation of dyadic spaces.[5]

References

  1. ^ a b Efimov, B.A. (2001) [1994], "Dyadic compactum", Encyclopedia of Mathematics, EMS Press
  2. ^ Efimov, B.A. (2001) [1994], "Dyadic space", Encyclopedia of Mathematics, EMS Press
  3. ^ Engelking, Ryszard (1977). General Topology. Monografie Matematyczne. Vol. 60. Warsaw: PWN. p. 231. Zbl 0373.54002.
  4. ^ T. C. Przymusinski, Products of normal spaces, Ch. XVIII In K. Kunen and J.E. Vaughan (eds) Handbook of Set-Theoretic Topology. North-Holland, Amsterdam, 1984, p. 794.
  5. ^ a b Hart, Klaas Pieter; Nagata, Jun-iti; Vaughan, Jerry E. (2003). Encyclopedia of General Topology. Elsevier Science. pp. 13, 193. ISBN 978-0444503558.
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