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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.

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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.

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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.

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Summary The inequality ( n=2 Σn p-2 ^ f(n) │ p )≤C p ││f││ (0<p≤2) is proved for the one- and two-dimensional Ciesielski-Fourier coefficients of functions in Hardy spaces.

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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

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C p(X). Correspondingly a Valdivia compact space Y has the weight at most an infinite cardinal κ if and only if every point-finite family of nonempty open sets in C p(Y) has the cardinality at most κ, that is p(C p(Y)) ≦ κ. Besides, it was proved that w(Y) = p(C p(Y)) for every linearly ordered compact Y. In particular, a Valdivia compact space or linearly ordered compact space Y is metrizable if and only if p(C p(Y)) = ℵ0. This gives answer to a question of O. Okunev and V. Tkachuk.

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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

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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

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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

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