Ein Approximationssatz f�r Bairesche Funktionen

Grimeisen, Gerhard

doi:10.1007/bf01470961

Cited by 9 publications

(5 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…it is known that with one possible exception, 17 each missing arrow from I to J means that I ≤ K J . 18 Although Fin × Fin ≤ + K conv and Fin × Fin ≤ K conv, in many other cases in Diagram 2 we have that if I ≤ K J , then I ≤ + K J . It is well-known that ideals Fin, I 1/n , ED, ED fin , Ran, S are all F σ ideals.…”

Section: On Two Relations Of Ideals Which Distinguish Ideal γ-Setsmentioning

confidence: 96%

“…We recall the definition of the ideal Fin α introduced in [26,18], recently studied in [3,12,28]. Throughout the paper, the ideal K α is the ideal on limit α consisting of all subsets of ordinals smaller than α. Fin 1 is the ideal Fin.…”

Section: Finmentioning

confidence: 99%

“…It is not known whether Ran ≤ K S, see[6,7,19,20] 18. Under assumption that we added all arrows arising from transitivity.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Ideal approach to convergence in functional spaces

Bardyla¹,

Šupina²,

Zdomskyy³

2021

Preprint

View full text Add to dashboard Cite

We solve the last standing open problem from the seminal paper by J. Gerlits and Zs. Nagy [17], which was later reposed by A. Miller, T. Orenshtein and B. Tsaban. Namely, we show that under p = c there is a δ-set, which is not a γ-set. Thus we construct a set of reals A such that although C p (A), the space of all real-valued continuous functions on A, does not have Fréchet-Urysohn property, C p (A) still possesses Pytkeev property. Moreover, under CH we construct a π-set which is not a δ-set solving a problem by M. Sakai. In fact, we construct various examples of δ-sets, which are not γ-sets, satisfying finer properties parametrized by ideals on natural numbers. Finally, we distinguish ideal variants of Fréchet-Urysohn property for many different Borel ideals in the realm of functional spaces.

show abstract

Section: On Two Relations Of Ideals Which Distinguish Ideal γ-Setsmentioning

confidence: 96%

Section: Finmentioning

confidence: 99%

See 1 more Smart Citation

Ideal approach to convergence in functional spaces

Bardyla¹,

Šupina²,

Zdomskyy³

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…The idea of such filters comes from Katětov [6] and Grimeisen [7], who worked on this problem independently. Note that actually N 1 is the Fréchet filter F Fr and N 2 is the dual filter of the well known and extensively studied ideal Fin × Fin.…”

Section: Katětov Filtersmentioning

confidence: 99%

Ranks of F-limits of filter sequences

Kwela

Recław

2013

Journal of Mathematical Analysis and Applications

View full text Add to dashboard Cite

“…[5]) as well as Grimeisen and Katětov papers from the sixties (cf. [13], [15] and [16]). Later many papers were published in this area including [7], [17] and [27].…”

Section: Introductionmentioning

confidence: 99%

A note on a new ideal

Kwela

2015

Journal of Mathematical Analysis and Applications

View full text Add to dashboard Cite

In this paper we study a new ideal $\mathcal{WR}$. The main result is the following: an ideal is not weakly Ramsey if and only if it is above $\mathcal{WR}$ in the Kat\v{e}tov order. Weak Ramseyness was introduced by Laflamme in order to characterize winning strategies in a certain game. We apply result of Natkaniec and Szuca to conclude that $\mathcal{WR}$ is critical for ideal convergence of sequences of quasi-continuous functions. We study further combinatorial properties of $\mathcal{WR}$ and weak Ramseyness. Answering a question of Filip\'ow et al. we show that $\mathcal{WR}$ is not $2$-Ramsey, but every ideal on $\omega$ isomorphic to $\mathcal{WR}$ is Mon (every sequence of reals contains a monotone subsequence indexed by a $\mathcal{I}$-positive set)

show abstract

Ein Approximationssatz f�r Bairesche Funktionen

Cited by 9 publications

References 7 publications

Ideal approach to convergence in functional spaces

Ideal approach to convergence in functional spaces

Ranks of F-limits of filter sequences

A note on a new ideal

Contact Info

Product

Resources

About