mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

, a dyadic compactum is a Hausdorff

topological space In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance. More specifically, a topological space is a set whose elements are called points ...

that is the

continuous Continuity or continuous may refer to: Mathematics * Continuity (mathematics), the opposing concept to discreteness; common examples include ** Continuous probability distribution or random variable in probability and statistics ** Continuous ...

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of a product of

discrete two-point space In topology In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, wit ...

s, and a dyadic space is a topological space with a

compactification Compactification may refer to: * Compactification (mathematics), making a topological space compact * Compactification (physics), the "curling up" of extra dimensions in string theory See also * Compaction (disambiguation) Compaction may refer t ...

which is a dyadic compactum. However, many authors use the term ''dyadic space'' with the same meaning as ''dyadic compactum'' above. 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. Dyadic compacta and spaces satisfy the Suslin condition, and were introduced by Russian mathematician

Pavel Alexandrov Pavel Sergeyevich Alexandrov (russian: Па́вел Серге́евич Алекса́ндров), sometimes romanized ''Paul Alexandroff'' (7 May 1896 – 16 November 1982), was a Soviet mathematician. He wrote about three hundred papers, ma ...

. Polyadic spaces are generalisation of dyadic spaces.

References

Properties of topological spaces {{topology-stub