Wallman and Z-compactifications

Steiner, A. K.; Steiner, E. F.

doi:10.1215/s0012-7094-68-03526-6

Cited by 29 publications

(9 citation statements)

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“…But if Z e Z [u>(£, F')] then ZnTeF'so ZnT =Z'nT for some Z' eZKJ, J^)]. Thus Zn X=Z' n XeF and ^<=JF rom [15] it follows that u>iX, F)^oeiX, IS) and the desired equality results. 3.…”

Section: Preliminariesmentioning

confidence: 82%

Nest Generated Intersection Rings in Tychonoff Spaces

Steiner¹,

Steiner²

1970

Transactions of the American Mathematical Society

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“…But if Z e Z [u>(£, F')] then ZnTeF'so ZnT =Z'nT for some Z' eZKJ, J^)]. Thus Zn X=Z' n XeF and ^<=JF rom [15] it follows that u>iX, F)^oeiX, IS) and the desired equality results. 3.…”

Section: Preliminariesmentioning

confidence: 82%

Nest Generated Intersection Rings in Tychonoff Spaces

Steiner¹,

Steiner²

1970

Transactions of the American Mathematical Society

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“…Theorem 2.5 together with this result, gives the following: THEOREM 3.1. (Steiner and Steiner [16]). If Z, Z', are two normal bases on X then W(Z') g W(Z) if and only ifZ separates Z'.…”

Section: Hausdorff Wallman Compactificationsmentioning

confidence: 99%

Wallman compactifications and Wallman realcompactifications

Gagrat

Naimpally

1973

J. Aust. Math. Soc.

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In 1964 Frink [8] generalized Wallman's method [17] of compactification and asked the question: “Is every Hausdorff compactification of a Tychonoff space a Wallman compactification?”. This problem, which is as yet unsolved, has led to the discovery of a number of necessary and/or sufficient conditions for a Hausdorff compactification to be Wallman; (see Alò and Shapiro [2], [3], Banasĉhewski [6], Njåstad [13] and Steiner [15]). Recently Alò and Shapiro [4], [5] have generalized the Wallman procedure to discuss what they call Z*-realcompact spaces and Z*-realcompactification n(Z) corresponding to a countably productive (c.p.) normal base Z on X. Some further work has been done by Steiner and Steiner [14].

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“…It follows from [8] that the partially-ordered set ~ (X) (g~ ~< J~2 if and only if ~ _ ~,~) is isomorphic, to the partially-ordered set S* (X) under the correspondence ~ ~ co (~). Hence Proposition 1 gives the necessary and sufficient condition for existence of the minimal element in ~* (X) too.…”

Section: ) ~ O~ Then ~ (X Y) --= ~ (B) If Y ~ K (X) and Ymentioning

confidence: 99%