Strongly Hewitt spaces

Ka̧kol, Jerzy; Śliwa, Wiesław

doi:10.1016/s0166-8641(01)00063-3

Cited by 4 publications

(15 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Proposition 1 may suggest the following concept which originally has been introduced by Kakol andŚliwa [39].…”

Section: Proposition 3 a Completely Regular Topological Hausdorff Spamentioning

confidence: 99%

“…The proof presented below from [39] uses an argument of Negrepontis [51] concerning [27,Theorem 2.7].…”

Section: Definitionmentioning

confidence: 99%

“…The following general Theorem 1 below was obtained in [39], parts 1, 2, and [70] part 3. To get property 3 from Theorem 1 we need the following two lemmas.…”

Section: Propositionmentioning

confidence: 99%

“…In [39] we presented the following example of a strongly realcompact space which is not locally compact.…”

Section: Lemma 2 Each Unbounded Filterbasis F On a Topological Space mentioning

confidence: 99%

“…The following theorem from [39] describes strongly realcompact spaces in term of C(X ) and applies to characterize bornological and Baire-like spaces C c (X ) for locally compact spaces X . Recall that a lcs E is Baire-like [60] if for every increasing sequence (A n ) n of absolutely convex closed sets covering E there exists m ∈ N such that A m is a neighbourhood of zero in E.…”

Section: Lemma 2 Each Unbounded Filterbasis F On a Topological Space mentioning

confidence: 99%

See 4 more Smart Citations

On realcompact topological vector spaces

Ka̧kol

Pellicer

2011

RACSAM

View full text Add to dashboard Cite

This survey paper collects some of older and quite new concepts and results from descriptive set topology applied to study certain infinite-dimensional topological vector spaces appearing in Functional Analysis, including Fréchet spaces, (L F)-spaces, and their duals, (D F)-spaces and spaces of continuous real-valued functions C(X ) on a completely regular Hausdorff space X . Especially (L F)-spaces and their duals arise in many fields of Functional Analysis and its applications, for example in Distributions Theory, DifferentialEquations and Complex Analysis. The concept of a realcompact topological space, although originally introduced and studied in General Topology, has been also studied because of very concrete applications in Linear Functional Analysis.

show abstract

“…Proposition 1 may suggest the following concept which originally has been introduced by Kakol andŚliwa [39].…”

Section: Proposition 3 a Completely Regular Topological Hausdorff Spamentioning

confidence: 99%

“…The proof presented below from [39] uses an argument of Negrepontis [51] concerning [27,Theorem 2.7].…”

Section: Definitionmentioning

confidence: 99%

“…The following general Theorem 1 below was obtained in [39], parts 1, 2, and [70] part 3. To get property 3 from Theorem 1 we need the following two lemmas.…”

Section: Propositionmentioning

confidence: 99%

“…In [39] we presented the following example of a strongly realcompact space which is not locally compact.…”

Section: Lemma 2 Each Unbounded Filterbasis F On a Topological Space mentioning

confidence: 99%

Section: Lemma 2 Each Unbounded Filterbasis F On a Topological Space mentioning

confidence: 99%

See 3 more Smart Citations

On realcompact topological vector spaces

Ka̧kol

Pellicer

2011

RACSAM

View full text Add to dashboard Cite

show abstract

Some Aspects in the MathematicalWork of Jerzy K a̧ kol

Pellicer

Moll

2014

Springer Proceedings in Mathematics &Amp; Statistics

View full text Add to dashboard Cite

Weak barrelledness for C(X) spaces

Ka̧kol

Saxon

Todd

2004

Journal of Mathematical Analysis and Applications

Self Cite

View full text Add to dashboard Cite

Buchwalter and Schmets reconciled C c (X) and C p (X) spaces with most of the weak barrelledness conditions of 1973, but could not determine if ℵ 0 -barrelled ⇔ ∞ -barrelled for C c (X). The areas grew apart. Full reconciliation with the fourteen conditions adopted by Saxon and Sánchez Ruiz needs their 1997 characterization of Ruess' property (L), which allows us to reduce the C c (X) problem to its 1973 status and solve it by carefully translating the topology of Kunen (1980) andvan Mill (1982) to find the example that eluded Buchwalter and Schmets. The more tractable C p (X) readily partitions the conditions into just two equivalence classes, the same as for metrizable locally convex spaces, instead of the five required for C c (X) spaces. Our paper elicits others, soon to appear, that analytically characterize when the Tychonov space X is pseudocompact, or Warner bounded, or when C c (X) is a df -space (Jarchow's 1981 question).

show abstract

Strongly Hewitt spaces

Cited by 4 publications

References 9 publications

On realcompact topological vector spaces

On realcompact topological vector spaces

Some Aspects in the MathematicalWork of Jerzy K a̧ kol

Weak barrelledness for C(X) spaces

Contact Info

Product

Resources

About