Wallman-type compactifications on 0-dimensional spaces

Su, Li

doi:10.1090/s0002-9939-1974-0339079-9

Cited by 5 publications

(2 citation statements)

References 12 publications

(3 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Hence 3f has property (a). It turns out that &>(££) is a zero-dimensional Wallman-type compactification of X and v{2£) is N-compact (see Su (1974), Theorem D).…”

Section: S C X -Z W H I C H Is In St (By (Iii)) T H U S W E H a V E mentioning

confidence: 99%

Round subsets of Wallman-type compactifications

1976

J. Aust. Math. Soc.

View full text Add to dashboard Cite

Let 2T be a normal base of a Tychonoff space X and w(3t) (v(3C)) denote the Wallman-type (real-) compactification of X generated by 3t. This Wallman-type compactification is known to associate with a unique proximity S. A 3. -filter &• is round if for each F £^ there is a n F G £^ such that F 0 E(X -F). A subset A of (o(3t) is called a round subset of (2?) are introduced. We also prove that the intersection of all the free 2T-ultrafilters is 9 = {Z e Z: C\ X (X -Z) is compact} iff o>(S)-X is a round subset of &>(2T); if 3T is a separating nest generated intersection ring with property (a) then w(S)-v(3?) is a round subset of u>(2).

show abstract

“…Hence 3f has property (a). It turns out that &>(££) is a zero-dimensional Wallman-type compactification of X and v{2£) is N-compact (see Su (1974), Theorem D).…”

Section: S C X -Z W H I C H Is In St (By (Iii)) T H U S W E H a V E mentioning

confidence: 99%

Round subsets of Wallman-type compactifications

1976

J. Aust. Math. Soc.

View full text Add to dashboard Cite

show abstract

“…When E is the real line, the projective maximum of (1) is the Stone-Cech compactification, and, when E is the countably infinite discrete space, it is the Banaschewski zero-dimensional compactification [2]. We note here that uniformities on E-completely regular spaces have been discussed (especially when E is zero-dimensional) in [1], [2], and [5], and E-completely regular Hausdorff compactifications for general spaces E are discussed in [11], [14], and [15].…”

mentioning

confidence: 99%

Rich Proximities and Compactifications

Carlson

1981

Can. j. math.

View full text Add to dashboard Cite

Each Hausdorff compactification of a given Tychonoff space is the Smirnov compactification associated with a compatible proximity on the space. Also each realcompactification of a given Tychonoff space is the underlying topological space of the completion of a compatible uniformity on the space. But if T is a realcompactification of a Tychonoff space X which is contained in a particular compactification Z of X, then it is not always possible to find a compatible uniformity on X such that T is the underlying topological space of the completion of (X, ) and induces the proximity on X associated with Z. We shall call a Hausdorff compactification Z of a Tychonoff space X a rich compactification of X (and the associated proximity on X a rich proximity) if every realcompactification of X contained in Z can be obtained as the underlying topological space of the completion of a compatible uniformity on X which induces the proximity on X associated with Z.

show abstract

Rings and sheaves

Vechtomov¹

1995

J Math Sci

View full text Add to dashboard Cite

Wallman-type compactifications on 0-dimensional spaces

Abstract: Abstract.Let E be Hausdorff O-dimensional, 3> the discrete space {0, 1}, and J' the discrete space of all nonnegative integers.

Cited by 5 publications

References 12 publications

Round subsets of Wallman-type compactifications

Round subsets of Wallman-type compactifications

Rich Proximities and Compactifications

Rings and sheaves

Contact Info

Product

Resources

About