The main result of this paper is that, under PFA, for every regular space X with F(X) = \omega we have |X| \le w(X)^\omega; in particular, w(X) \le \mathfrak {c} implies |X| \le \mathfrak {c}. This ...complements numerous prior results that yield consistent examples of even compact Hausdorff spaces X with F(X) = \omega such that w(X) = \mathfrak {c} and |X| = 2^\mathfrak {c}.
We also show that regularity cannot be weakened to the Hausdorff property in this result because we can find in ZFC a Hausdorff space X with F(X) = \omega such that w(X) = \mathfrak {c} and |X| = 2^\mathfrak {c}. In fact, this space X has the strongly anti-Urysohn (SAU) property that any two infinite closed sets in X intersect, which is much stronger than F(X) = \omega. Moreover, any non-empty open set in X also has size 2^\mathfrak {c}, and thus our example answers one of the main problems of both Juhász, Soukup, and Szentmiklóssy Topology Appl. 213 (2016), pp. 8–23 and Juhász, Shelah, Soukup, and Szentmiklóssy Topology Appl. 323 (2023), Paper No. 108288, 15 pp. by providing in ZFC a SAU space with no isolated points.
On \sigma-countably tight spaces MILL, ISTVÁN JUHÁSZ AND JAN VAN
Proceedings of the American Mathematical Society,
01/2018, Letnik:
146, Številka:
1
Journal Article
Recenzirano
Odprti dostop
dense or finitely many arbitrary countably tight subspaces. The question if every infinite homogeneous and \sigma -countably tight compactum has cardinality \mathfrak{c} remains open.
Trastuzumab is a recombinant antibody drug that is widely used for the treatment of breast cancer. Despite encouraging clinical
results, some cancers are primarily resistant to trastuzumab, and a ...majority of those initially responding become resistant
during prolonged treatment. The mechanisms of trastuzumab resistance have not been fully understood. We examined the role
of antibody-dependent cellular cytotoxicity (ADCC) using JIMT-1 cells that are ErbB2 positive but intrinsically resistant
to trastuzumab in vitro . Unexpectedly, in experiments mimicking adjuvant therapy of submacroscopic disease in vivo (JIMT-1 cells inoculated s.c. in severe combined immunodeficiency mice), trastuzumab was able to inhibit the outgrowth of
macroscopically detectable xenograft tumors for up to 5–7 weeks. The effect is likely to be mediated via ADCC because trastuzumab-F(ab′) 2 was ineffective in this model. Moreover, in vitro ADCC reaction of human leukocytes was equally strong against breast cancer cells intrinsically sensitive (SKBR-3) or resistant
(JIMT-1) to trastuzumab or even against a subline of JIMT-1 that was established from xenograft tumors growing despite trastuzumab
treatment. These results suggest that ADCC may be the predominant mechanism of trastuzumab action on submacroscopic tumor
spread. Thus, measuring the ADCC activity of patient's leukocytes against the tumor cells may be a relevant predictor of clinical
trastuzumab responsiveness in vivo . Mol Cancer Ther 2007;6(7):2065–72
Introduction Globally, from the age of 14, the dropout rate of young athletes is high in all sports games in Hungary. The reasons for dropping out are complex, however parental support is critical to ...succeed or continue, especially after failure or injury. The present study explored the main effects of sports injury and sport participation stage on parental involvement in sports. Methods 1,174 parents and 690 athletes completed our questionnaire, which contains questions on young players’ sport participation, injury background and Parental Involvement in Sport Questionnaire. Results Parents’ self-perceived level of involvement differed from the parental involvement perceived by their children. The significant predictors were the person who completed, the parent/athlete, the athlete’s previous sports injury and the child’s current stage of sport participation. In Directive Behavior, the main effect of stages is only seen in parents whose child has been injured. In the sample of injured athletes, the rate of perceived parental Praise and Understanding tends to be lower in the specializing stage. Discussion Our findings suggest that these two behaviors could be part of the same parenting style, which requires further investigation. The results expand the existing knowledge of the complexity of parents’ involvement in children’s sports careers. These findings have implications beyond parental psychoeducation impacting the work of coaches, sports physicians and rehabilitation experts.
The aim of this paper is to consider questions concerning the possible maximum cardinality of various separable pseudoradial (in short: SP) spaces. The most intriguing question here is if there is in ...ZFC a regular (or just Hausdorff) SP space of cardinality >c. While this question is left open, we establish a number of non-trivial results that we list below.•It is consistent with MA+c=ℵ2 that there is a countably tight and compact SP space of cardinality 2c.•If κ is a measurable cardinal then in the forcing extension obtained by adding κ many Cohen reals, every countably tight regular SP space has cardinality at most c.•If κ>ℵ1 Cohen reals are added to a model of GCH then in the extension every pseudocompact SP space with a countable dense set of isolated points has cardinality at most c.•If c≤ℵ2 then there is a 0-dimensional SP space with a countable dense set of isolated points that has cardinality greater than c.
On a problem of Angelo Bella Juhász, István; Soukup, Lajos; Szentmiklóssy, Zoltán
Topology and its applications,
12/2023, Letnik:
340
Journal Article
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The main result of this note is the following theorem.
If X is any Hausdorff space withκ=Fˆ(X)⋅μˆ(X)thenL(X<κ)≤ϱ(κ).
Here Fˆ(X) is the smallest cardinal φ so that |S|<φ for any set S that is free in ...X and μˆ(X) is the smallest cardinal μ so that, for every set S that is free in X, any open cover of S‾ has a subcover of size <μ. Moreover, X<κ is the G<κ-modification of X and ϱ(κ)=min{ϱ:ϱ<κ=ϱ}.
As a corollary we obtain that if X is a linearly Lindelöf regular space of countable tightness then L(Xδ)≤c, provided that c=2<c. This yields a consistent affirmative answer to a question of Angelo Bella.
A space has σ-compact tightness if the closures of σ-compact subsets determine the topology. We consider a dense set variant that we call densely k-separable. We consider the question of whether ...every densely k-separable space is separable. The somewhat surprising answer is that this property, for compact spaces, implies that every dense set is separable. The path to this result relies on the known connections established between π-weight and the density of all dense subsets, or more precisely, the cardinal invariant δ(X).
The main objective of my research was to explore whether there are differences between the personality of salespeople working in the finance and insurance sectors and that of ‘average' Hungarian ...citizens. In answering this question, I relied on the 21 respective dimensions of the Short California Psychological Inventory. Accordingly, I examined a sample of 1,000 salespeople employed at banks, insurance companies, building societies, financial consultancy firms, factoring and leasing companies, savings associations and companies listed on the stock exchange. As a result of the application of a one-sample t-test in breakdown by gender, it could be concluded that, apart from the results obtained for Capacity for Status, Ego Strength, Good Impression and Communality for women included in the sample, and Capacity for Status and Psychological-Mindedness for men included in the sample, which do not show a statistically justifiable divergence from standard values, the rest of the values do show a significant divergence. Consequently, in the majority of the 21 personality dimensions, divergences can be noted between the test sample and the standard values. These findings should definitely be taken into account during human resource management, and particularly during employee selection, in the financial sector.
It is an interesting, maybe surprising, fact that different dense subspaces of even “nice” topological spaces can have different densities. So, our aim here is to investigate the set of densities of ...all dense subspaces of a topological space
X
that we call the double density spectrum of
X
and denote by dd(
X
).
We improve a result from 1 by showing that dd(
X
) is always
ω
-closed (i.e., countably closed) if
X
is Hausdorff.
We manage to give complete characterizations of the double density spectra of Hausdorff and of regular spaces as follows.
Let
S
be a non-empty set of infinite cardinals. Then
S
= dd(
X
) holds for a Hausdorff space
X
iff
S
is
ω
-closed and
S
= dd(
X
) holds for a regular space
X
iff
S
is
ω
-closed and sup
S
≤ 2
min
S
.
We also prove a number of consistency results concerning the double density spectra of compact spaces. For instance:
If
κ
= cf(
κ
)embeds in
and
S
is any set of uncountable regular cardinals <
κ
with ∣
S
∣ < min
S
, then there is a compactum
C
such that {
ω, κ
}∪
S
⊂ dd(
C
), moreover
λ
∉ dd(
C
) whenever ∣
S
∣ +
ω
< cf(λ) <
κ
and cf(λ) ∉
S
.
It is consistent to have a separable compactum
C
such that dd(
C
) is not
ω
1
-closed.
The microbial community exhibits remarkable diversity on topographically distinct skin regions, which may be accompanied by differences in skin immune characteristics. Our aim was to compare the ...immune milieu of healthy sebaceous gland-rich (SGR) and sebaceous gland-poor skin areas, and to analyze its changes in an inflammatory disease of SGR skin. For this purpose, immunohistochemical, immunocytochemical, and quantitative real-time PCR analyses of thymic stromal lymphopoietin (TSLP) and other cytokines, phenotypic immune cell markers and transcription factors were carried out in samples from sebaceous gland-poor, SGR skin and from papulopustular rosacea. TSLP mRNA and protein production was also studied in cultured keratinocytes. In SGR skin, higher TSLP expression, dendritic cell appearance without prominent activation, and T cell presence with IL-17/IL-10 cytokine milieu were detected compared with sebaceous gland-poor skin. Linoleic acid, a major sebum component, was found to induce TSLP expression dose-dependently in keratinocytes. In papulopustular rosacea, significantly decreased TSLP level and influx of inflammatory dendritic cells and T cells with IL-17/interferon-γ cytokine milieu were observed. According to our results, SGR skin is characterized by a distinct, noninflammatory immune surveillance, which may explain the preferred localization of inflammatory skin diseases, and can influence future barrier repair therapeutic concepts.
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