Regular matrices and -sets in . II

Author:
Robert E. Atalla

Journal:
Proc. Amer. Math. Soc. **115** (1992), 141-144

MSC:
Primary 40C05

MathSciNet review:
1094496

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Abstract: It was discovered by Henriksen and Isbell that the support in of a regular matrix is a -set. We study conditions under which a -subset of a matrix support set contains another matrix support set.

**[Al]**R. E. Atalla,*Regular matrices and 𝑃-sets in 𝛽𝑁\𝑁*, Proc. Amer. Math. Soc.**37**(1973), 157–162. MR**0324655**, 10.1090/S0002-9939-1973-0324655-9**[A2]**Robert E. Atalla,*Problems on 𝑃-sets and 𝑃₁-sets*, Questions Answers Gen. Topology**8**(1990), no. 2, 383–385. MR**1065286****[FSZ]**R. Frankiewicz, S. Shelah, and P. Zbierski,*Embeddings of Boolean algebras in**finite*, Notices Amer. Math. Soc.**10**(1989), 399.**[FT]**F. Terpe and Ju. Flaksmaĭer,*Some applications of extension theory for topological spaces and of measure theory*, Uspehi Mat. Nauk**32**(1977), no. 5(197), 125–162, 239 (Russian). Translated from the German by Ju. M. Smirnov. MR**0478106****[H]**P. Halmos,*Ergodic theory*, Chelsea Publ. Co., New York, 1956.**[HI]**M. Henriksen and J. Isbell,*Multiplicative summability methods and the Stone-Čech compactification*II, Notices Amer. Math. Soc.**11**(1964), 90-91.**[JK]**Winfried Just and Adam Krawczyk,*On certain Boolean algebras 𝒫(𝜔)/ℐ*, Trans. Amer. Math. Soc.**285**(1984), no. 1, 411–429. MR**748847**, 10.1090/S0002-9947-1984-0748847-1**[M]**Jan van Mill,*An introduction to 𝛽𝜔*, Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 503–567. MR**776630****[P]**Donald Plank,*On a class of subalgebras of 𝐶(𝑋) with applications to 𝛽𝑋𝑋*, Fund. Math.**64**(1969), 41–54. MR**0244953****[V]**A. I. Veksler and Z. T. Dikanova,*𝑃-sets in bicompacta*, Geometry and topology, No. 2 (Russian), Leningrad. Gos. Ped. Inst., Leningrad, 1974, pp. 46–58 (Russian). MR**0467699**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1992-1094496-8

Keywords:
Regular matrix,
support set of a matrix,
-set

Article copyright:
© Copyright 1992
American Mathematical Society