Nest Generated Intersection Rings in Tychonoff Spaces

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

doi:10.2307/1995391

Cited by 7 publications

(3 citation statements)

References 6 publications

(8 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Corollary 2.3 in [5] shows that the correspondence between the family Lf(X) of all bases on a space X and the associated Wallman compactifications is one-to-one. This is not the case between LP(X) and the associated Wallman realcompactiiications ([5], 3.13; [2], Corolla~ 4.1).…”

Section: Definitions and Basic Resultsmentioning

confidence: 99%

“…If A is an algebra on X, we write ~e(A) for the set {Z(f): fCA}. In [5] it is proved that the mapping A~s is a one-to-one correspondence between the family of all algebras on X and s On the other hand, from ([2], Theorem 2.5) a base on X is complete if and only if its associated algebra on X is isomorphic to C(Z) for some space Z. Thus, from the above Theorem it follows that if Y is an uncountable discrete space of nonmeasurable cardinal, there are infinitely many algebras on Y which are isomorphic to no C(Z).…”

Section: A Technique For Constructing Noncomplete Basesmentioning

confidence: 99%

“…An equivalent concept is the strong delta normal base due to ALb and SHAPIRO[1]. We adopt our notation and terminology from[1],[5] and our earlier paper[2]. ** Two extensions T: and T, of a space X are said to be equivalent if they are homeomc~phic via a map that leaves X pointwise fixed.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Noncomplete bases on discrete spaces

Blasco¹

1980

Acta Mathematica Academiae Scientiarum Hungaricae

View full text Add to dashboard Cite

Section: Definitions and Basic Resultsmentioning

confidence: 99%

Section: A Technique For Constructing Noncomplete Basesmentioning

confidence: 99%

See 1 more Smart Citation

Noncomplete bases on discrete spaces

Blasco¹

1980

Acta Mathematica Academiae Scientiarum Hungaricae

View full text Add to dashboard Cite

A note on 𝒵-realcompactifications

D'Aristotle¹

1972

Proc. Amer. Math. Soc.

View full text Add to dashboard Cite

Abstract.Orrin Frink showed that the real-valued functions over a Tychonoff space X which may be continuously extended to i3£) consisting of the iF-ultrafilters, is a Hausdorff compactification of A. By choosing different normal bases ¡£ for a noncompact space A, different Hausdorff compactifications of A may be obtained.In [1], Alo and Shapiro used ^-ultrafilters from a delta normal base (a normal base closed under countable intersections) to introduce a new space J?(â°) consisting of those ¿2f-ultrafilters with the countable intersection property. To each delta normal base 2£ on A there corresponds a delta normal base 2£* on fji^), and they have shown that every 2£*-ultrafilter with the countable intersection property is fixed, i.e., r¡i¡&) iŝ *-realcompact. For many delta normal bases 2£, r\i¡£) is realcompact in the usual sense but, in [5], it has been shown that this is not always the case.A real function/defined over a space X with normal base 3£ is said to be ¿^-uniformly continuous if for every positive epsilon there exists a finite open cover of A by iF-complements, on each of which the oscillation of /is less than epsilon. Frink showed that/may be continuously extended to o¡i&) if and only if/ is áT-uniformly continuous.

show abstract

Wallman-type compactifications on 0-dimensional spaces

Su¹

1974

Proc. Amer. Math. Soc.

View full text Add to dashboard Cite

show abstract

Nest Generated Intersection Rings in Tychonoff Spaces

Cited by 7 publications

References 6 publications

Noncomplete bases on discrete spaces

Noncomplete bases on discrete spaces

A note on 𝒵-realcompactifications

Wallman-type compactifications on 0-dimensional spaces

Contact Info

Product

Resources

About