On the separable quotient problem for Banach spaces

While the classic separable quotient problem remains open, we survey general results related to this problem and examine the existence of a particular infinitedimensional separable quotient in some Banach spaces of vector-valued functions, linear operators and vector measures. Most of the results presented are consequence of known facts, some of them relative to the presence of complemented copies of the classic sequence spaces c_0 and l_p, for 1 <= p <= \infty. Also recent results of Argyros - Dodos - Kanellopoulos, and Sliwa are provided. This makes our presentation supplementary to a previous survey (1997) due to Mujica

Bounded resolutions for spaces Cp(X) and a characterization in terms of X

An internal characterization of the Arkhangel’ski˘ı-Calbrixmain theorem from [4] is obtained by showing that the space Cp(X) of continuous real-valued functions on a Tychonoff space X is K-analytic framed in RX if and only if X admits a nice framing. This applies to show that a metrizable (or cosmic) space X is σ -compact if and only if X has a nice framing. We analyse a few concepts which are useful while studying nice framings. For example, a class of Tychonoff spaces X containing strictly Lindelöf Cˇ ech-complete spaces is introduced for which a variant of Arkhangel’ski˘ı-Calbrix theorem for σ-boundedness of X is shown

Spaces C(X)with ordered bases

[EN] The concept of Sigma-base of neighborhoods of the identity of a topological group G is introduced. If the index set Sigma subset of N-N is unbounded and directed (and if additionally each subset of Sigma which is bounded in N-N has a bound at Sigma) a base {U-alpha : alpha is an element of Sigma} of neighborhoods of the identity of a topological group G with U-beta subset of U-alpha whenever alpha <= beta with alpha, beta is an element of Sigma is called a Sigma-base (a Sigma(2)-base). The case when Sigma = N-N has been noticed for topological vector spaces (under the name of G-base) at [2]. If X is a separable and metrizable space which is not Polish, the space C-c(X) has a Sigma-base but does not admit any G-base. A topological group which is Frechet-Urysohn is metrizable iff it has a Sigma(2)-base of the identity. Under an appropriate ZFC model the space C-c (omega(1)) has a Sigma(2)-base which is not a G-base. We also prove that (i) every compact set in a topological group with a Sigma(2)-base of neighborhoods of the identity is metrizable, (ii) a C-p (X) space has a Sigma(2)-base iff X is countable, and (iii) if a space C-c(X) has a Sigma(2)-base then X is a C-Suslin space, hence C-c(X)is angelic. (C) 2016 Elsevier B.V. All rights reserved.Supported by Grant PROMETEO/2013/058 of the Conselleria de Education, Investigacion, Cultura y Deportes of Generalitat Valenciana. The second author also supported by the GACR Project 16-34860L and RVO: 67985840Ferrando, JC.; Kakol, J.; López Pellicer, M. (2016). Spaces C(X)with ordered bases. Topology and its Applications. 208:30-39. https://doi.org/10.1016/j.topol.2016.05.006S303920

Compact covers and function spaces

For a Tychonoff space X, we denote by Cp(X) and Cc(X) the space of continuous real-valued functions on X equipped with the topology of pointwise convergence and the compact-open topology respectively. Providing a characterization of the Lindelof $Sigma$-property of X in terms of Cp(X), we extend Okunev's results by showing that if there exists a surjection from Cp(X) onto Cp(Y) (resp. from Lp(X) onto Lp(Y)) that takes bounded sequences to bounded sequences, then $nu$Y is a Lindelof $Sigma$-space (respectively K-analytic) if $nu$X has this property. In the second part, applying Christensen's theorem, we extend Pelant's result by proving that if X is a separable completely metrizable space and Y is first countable, and there is a quotient linear map from Cc(X) onto Cc(Y), then Y is a separable completely metrizable space.We study also a non-separable case, and consider a different approach to the result of J. Baars, J. de Groot, J. Pelant and V. Valov, which is based on the combination of two facts: Complete metrizability is preserved by lp-equivalence in the class of metric spaces (J. Baars, J. de Groot, J. Pelant). If X is completely metrizable and lp-equivalent to a first-countable Y, then Y is metrizable (V. Valov). Some additional results are presented.The research was supported for the first named author by National Center of Science, Poland, Grant No. N N201 605340, and for the first and second named authors by Generalitat Valenciana, Conselleria d'Educacio i Esport, Spain, Grant PROMETEO/2013/058.Kakol, J.; López Pellicer, M.; Okunev, O. (2014). Compact covers and function spaces. Journal of Mathematical Analysis and Applications. 411(1):372-380. https://doi.org/10.1016/j.jmaa.2013.09.046S372380411

Orthogonal sequences in non-archmedean locally convex spaces

AbstractThe problem of the existence of (orthogonal) bases and basic sequences in non-archimedean locally convex spaces is studied. To this end we derive a characterization of compactoidity in terms of orthogonal sequences (Theorem 2.2)

Magnetic properties of the Old Crow tephra: Identification of a complex iron titanium oxide mineralogy

International audience[1] The mineralogy and grain-size distribution of the Fe-Ti oxide population of the Old Crow tephra bed, outcropping at the Halfway House loess deposit in central Alaska, are characterized through multiple low-and high-temperature magnetization experiments. The characterization is facilitated by heavy liquid separation of the bulk sample into a low-density ( 0.8 and may play an equally important role as magnetic indicator of titanomagnetite. Furthermore, we demonstrate the ability of low-temperature magnetism to locate a 1 mm thick tephra bed dispersed in loess over 10 cm depth, through the identification of very low concentrations of a titanohematite phase with y = 0.9. The potential for advancing regional correlation of sedimentary deposits through the identification of Fe-Ti oxides common to tephra beds by low-temperature magnetism is illustrated in this study. INDEX TERMS: 1540 Geomagnetism and Paleomagnetism: Rock and mineral magnetism; 1512 Geomagnetism and Paleomagnetism: Environmental magnetism; 1519 Geomagnetism and Paleomagnetism: Magnetic mineralogy and petrology; 8404 Volcanology: Ash deposits; 5109 Physical Properties of Rocks: Magnetic and electrical properties; KEYWORDS: low-temperature magnetism, frequency and amplitude dependence of AC susceptibility, ilmenite-hematite and magnetite-ulvospinel solid solution series, tephra, stratigraphic correlatio

cis sequence effects on gene expression

<p>Abstract</p> <p>Background</p> <p>Sequence and transcriptional variability within and between individuals are typically studied independently. The joint analysis of sequence and gene expression variation (genetical genomics) provides insight into the role of linked sequence variation in the regulation of gene expression. We investigated the role of sequence variation in <it>cis </it>on gene expression (<it>cis </it>sequence effects) in a group of genes commonly studied in cancer research in lymphoblastoid cell lines. We estimated the proportion of genes exhibiting <it>cis </it>sequence effects and the proportion of gene expression variation explained by <it>cis </it>sequence effects using three different analytical approaches, and compared our results to the literature.</p> <p>Results</p> <p>We generated gene expression profiling data at N = 697 candidate genes from N = 30 lymphoblastoid cell lines for this study and used available candidate gene resequencing data at N = 552 candidate genes to identify N = 30 candidate genes with sufficient variance in both datasets for the investigation of <it>cis </it>sequence effects. We used two additive models and the haplotype phylogeny scanning approach of Templeton (Tree Scanning) to evaluate association between individual SNPs, all SNPs at a gene, and diplotypes, with log-transformed gene expression. SNPs and diplotypes at eight candidate genes exhibited statistically significant (p < 0.05) association with gene expression. Using the literature as a "gold standard" to compare 14 genes with data from both this study and the literature, we observed 80% and 85% concordance for genes exhibiting and not exhibiting significant <it>cis </it>sequence effects in our study, respectively.</p> <p>Conclusion</p> <p>Based on analysis of our results and the extant literature, one in four genes exhibits significant <it>cis </it>sequence effects, and for these genes, about 30% of gene expression variation is accounted for by <it>cis </it>sequence variation. Despite diverse experimental approaches, the presence or absence of significant <it>cis </it>sequence effects is largely supported by previously published studies.</p