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ArticleOriginal scientific text

Title

On matrix rapid filters

Authors 1, 2

Affiliations

  1. Department of Mathematics, Ohio University, Athens, Ohio 45701
  2. Slovak Academy of Sciences, Košice, Slovakia

Abstract

Galois-Tukey equivalence between matrix summability and absolute convergence of series is shown and an alternative characterization of rapid ultrafilters on ω is derived.

Bibliography

  1. [A] R. Atalla, Regular matrices and P-sets in βN\N, Proc. Amer. Math. Soc. 37 (1973), 157-162.
  2. [M] G. Mokobodzki, Ultrafiltres rapides sur N. Construction d'une densité relative de deux potentiels comparables, in: Séminaire Brelot-Choquet-Deny (Théorie du Potentiel), 12e année, 1967/68, no. 12, pp. 12-01 to 12-22.
  3. [R] J. Rainwater, Regular matrices with nowhere dense supports, Proc. Amer. Math. Soc. 29 (1971), 361.
  4. [V1] P. Vojtáš, Generalized Galois-Tukey-connections between explicit relations on classical objects of real analysis, in: Israel Math. Conf. Proc. 6, 1993, 619-643.
  5. [V2] P. Vojtáš, ω* and absolutely divergent series, Topology Proc. 19 (1994), 335-348.
Fundamenta Mathematicae
1997/154/2
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Pages:
177-182
Main language of publication
English
Received
1996-05-04
Published
1997
Exact and natural sciences