On locally convex vector spaces of continuous functions

Shirota, Taira

doi:10.3792/pja/1195526112

Cited by 69 publications

(29 citation statements)

References 7 publications

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“…For example, letting R denote the real numbers, C(R) is barrelled and therefore has the Mackey topology (see [10] or [12]). The theorem has some point, however, since not every C(X) has the Mackey topology.…”

Section: Where Hec(k) and H' Is Any Continuous Extension Of H To All mentioning

confidence: 99%

“…According to a result of Nachbin [10] and Shirota [12], C(X), for X completely regular Hausdorff, is bornological if, and only if, X is realcompact. From the fact that a complete bornological space is barrelled, we have: COROLLARY …”

Section: Let E Be a Complete *-Algebra Then E Is Topologically *-Isomentioning

confidence: 99%

“…Note that, by (6.1), a closed C(M)-pseudocompact subset of M is compact. According to a well known result due independently to Nachbin [10] and Shirota [12], the real space C(X, R) is barrelled if, and only if, every C(X, ϋ? )-pseudocompact subset of X is compact.…”

Section: Let X Be a Realcompact Space And T A Topology On C(x) Such Tmentioning

confidence: 99%

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Functional representation of topological algebras

Morris¹,

Wulbert²

1967

Pacific J. Math.

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Section: Where Hec(k) and H' Is Any Continuous Extension Of H To All mentioning

confidence: 99%

Section: Let E Be a Complete *-Algebra Then E Is Topologically *-Isomentioning

confidence: 99%

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Functional representation of topological algebras

Morris¹,

Wulbert²

1967

Pacific J. Math.

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“…by Manuel VALDIVIA L. Nachbin [5] and T. Shirota [6], give an answer to a problem proposed by N. Bourbaki [1] and J. Dieudonne [2], giving an example of a barrelled space, which is not bornological. Posteriorly some examples of nonbornological barrelled spaces have been given, e.g.…”

Section: On Nonbornological Barrelled Spacesmentioning

confidence: 94%

On nonbornological barrelled spaces

Valdivia¹

1972

Annales De L’institut Fourier

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“…Nachbin [12] and Shirota [16] give the following characterizations for CC(A) (the vector space C(A) provided with the compact-open topology):…”

mentioning

confidence: 99%

On 𝜇-spaces and 𝑘_{𝑅}-spaces

Blasco¹

1977

Proc. Amer. Math. Soc.

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Abstract. In this paper it is proved that when .¥/ is a kR-space then pX (the smallest subspace of ßX containing X with the property that each of its bounded closed subsets is compact) also is a /cÄ-space; an example is given of a kR -space X such that its Hewitt realcompactification, vX, is not a /cÄ-space. We show with an example that there is a non-/cÄ-space X such that vX and pX are kR-spaces. Also we answer negatively a question posed by Buchwalter: Is pX the union of the closures in vX of the bounded subsets of A"? Finally, without using the continuum hypothesis, we give an example of a locally compact space X of cardinality n, such that vX is not a /c-space.Introduction. The topological spaces used here will always be completely regular Hausdorff spaces. If X is a topological space we write C(X) for the ring of the continuous real-valued functions on X, and ßX (resp. vX) for the Stone-Cech compactification (resp. Hewitt realcompactification) of X. A

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On locally convex vector spaces of continuous functions

Cited by 69 publications

References 7 publications

Functional representation of topological algebras

Functional representation of topological algebras

On nonbornological barrelled spaces

On 𝜇-spaces and 𝑘_{𝑅}-spaces

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