Compactifications determined by subsets of C∗(X), II

Ball, B. J.; Yokura, Shoji

doi:10.1016/0166-8641(83)90041-x

Cited by 7 publications

(7 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the classical theory of Hausdorff compactifications in ZFC, an important role is played by evaluation mappings into Tychonoff cubes (cf. e. g. [BY1]- [BY3], [Bl], [W1]- [W3]). Let us recall that, for an indexed set F = {f j : j ∈ J} of mappings f j : X → Y j , the evaluation mapping e F : X → j∈J Y j is defined by: [e F (x)](j) = f j (x) for x ∈ X and j ∈ J.…”

Section: Continuous Extensions Of Mappingsmentioning

confidence: 99%

“…If X is a topological space, {Y j : j ∈ J} is a collection of topological spaces and F = {f j : j ∈ J} where each f j is a mapping from X into Y j , there are nice necessary and sufficient conditions for e F to be a homeomorphic embedding (cf. e. g. [Ch], [BY1]- [BY3], [W1]- [W3] and 2.3.D of [En]); however, the following interesting problem is new and unsolved:…”

Section: Embeddings Into Productsmentioning

confidence: 99%

“…e. g. [BY1]- [BY3], [Bl], [W1]- [W3]). Let us recall that, for an indexed set F = {f j : j ∈ J} of mappings f j : X → Y j , the evaluation mapping e F : X → j∈J Y j is defined by: [e F (x)](j) = f j (x) for x ∈ X and j ∈ J.…”

Section: Embeddings Into Productsmentioning

confidence: 99%

See 2 more Smart Citations

Compactness and compactifications in generalized topology

Piękosz

Wajch

2015

Topology and its Applications

View full text Add to dashboard Cite

A generalized topology in a set X is a collection Cov X of families of subsets of X such that the triple (X, Cov X , Cov X ) is a generalized topological space in the sense of Delfs and Knebusch. In this work, notions of topological and admissible compactness of generalized topologies are introduced to begin and investigate a theory of compactifications, in particular, of Wallman type in the category of weakly normal generalized topological spaces. Among other facts, we prove in ZF that the ultrafilter theorem (in abbreviation UFT) holds if and only if all Wallman extensions of every weakly normal generalized topological space are compact. In consequence, we develop the theory of compactifications in ZF+UFT when it is not necessary to use AC, while ZF is not enough.

show abstract

Section: Continuous Extensions Of Mappingsmentioning

confidence: 99%

Section: Embeddings Into Productsmentioning

confidence: 99%

See 1 more Smart Citation

Compactness and compactifications in generalized topology

Piękosz

Wajch

2015

Topology and its Applications

View full text Add to dashboard Cite

show abstract

“…Denote by (C h (X)) h ′ the set of extensions of Higson functions on X to h ′ (X). By [16] the C * -algebra of Higson functions C h (X) determines the compactification h ′ (X) if and only if (C h (X)) h ′ separates points of ν ′ (X).…”

Section: Corollary 15 If Mcoarse Denotes the Category Of Metric Space...mentioning

confidence: 99%

“…x → (ϕ(x)) ϕ the evaluation map for X. Note e C h (X) is a topological embedding and ν(X) := e C h (X) (X) \ e C h (X) (X) by [16]. A point p ∈ ν(X) is represented by a net (x i ) i such that for every Higson function ϕ ∈ C h (X) the net ϕ(x i ) i converges in R. Define F i := {x j : j ≥ i} for every i.…”

Section: Corollary 15 If Mcoarse Denotes the Category Of Metric Space...mentioning

confidence: 99%