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Abstract
For a Tychonoff space X, we denote by C p(X) the space of real-valued continuous functions with the topology of pointwise convergence. We show that (a) Arhangel℉skii℉s property (α 2) and the Ramsey property introduced by Nogura and Shakhmatov are equivalent for C p(X), (b) the Ramsey property and Nyikos’ property (α 3/2) are not equivalent for C p(X). These results answer questions posed by Shakhmatov. Concerning properties (α i) for C p(X), some results on Scheepers’ conjecture are also given.
Abstract
We prove that there are Tychonoff spaces X for which p(Cp(X)) =ϖ and Cp(X) is a Lindelf Σ-space while the network weight of X is uncountable. This answers Problem 75 from [4]. An example of a space Y is given such that p(Y)=ϖ and Cp(Y) is a Lindelf Σ-space, while the network weight of Y is uncountable. This gives a negative answer to Problem 73 from [4]. For a space X with one non-isolated point a necessary and sufficient condition in terms of the topology on X is given for Cp(X) to have countable point-finite cellularity.
Summary We prove that, for any Tychonoff X, the space C p(X) is K-analytic if and only if it has a compact cover {K p: p ? ??} such that K p subset K q whenever p,q ? ?? and p = q. Applying this result we show that if C p(X) is K-analytic then C p(?X) is K-analytic as well. We also establish that a space C p(X) is K-analytic and Baire if and only if X is countable and discrete.
Summary The inequality ( ∞ n=2 Σn p-2 │ ^ f(n) │ p )≤C p ││f││ H (0<p≤2) is proved for the one- and two-dimensional Ciesielski-Fourier coefficients of functions in Hardy spaces.
Abstract
We prove that every point-finite family of nonempty functionally open sets in a topological space X has the cardinality at most an infinite cardinal κ if and only if w(X) ≦ κ for every Valdvia compact space Y
received) and a suitable measure or proxy for quality (say, impact, defined as the ratio of citations to publications, i.e., i = C/P ). The neologism, quasity, needs some explanation. Table 1 shows analogies from classical mechanics, electrical
citing Smalley. Method There are PT, PN, TI, AU, AE, GA, AB, MC, IP, PD, AD, FD, PI, FS, CP, CR, UT and some other bibliographic items in a patent document in the database of DII. Among them, the item CP, cited patents in prior
for the analysis of scientific publications. Sun et al. ( 2006 ) introduced a dynamic tensor analysis (DTA) method and applied multi-way latent semantic indexing to the analysis of DBLP data. Dunlavy et al. ( 2006 ) applied CANDECOMP/PARAFAC (CP
