On ∞\infty-convex sets in spaces of scatteredly continuous functions

Given a topological space $X$, we study the structure of $\infty$-convex subsets in the space $SC_p(X)$ of scatteredly continuous functions on $X$. Our main result says that for a topological space $X$ with countable strong fan tightness, each potentially bounded $\infty$-convex subset $F\subset SC_p(X)$ is weakly discontinuous in the sense that each non-empty subset $A\subset X$ contains an open dense subset $U\subset A$ such that each function $f|U$, $f\in F$, is continuous. This implies that $F$ has network weight $nw(F)\le nw(X)$.Comment: 10 page

Density topology and pointwise convergence

[EN] We shall show that the space of all approximately continuous functions with the topology of pointwise convergence is not homeomorphic to its category analogue.Wilczynski, W. (2003). Density topology and pointwise convergence. Applied General Topology. 4(2):509-512. doi:10.4995/agt.2003.2048.SWORD50951242A.V. Arkhangel'skii, Prostranstwa funktsii v topologii potochechnoi skhodimosti (Spaces of functions in the topology of pointwise convergence), General topology, spaces of functions and dimension, MGU Moskva 1985 (in Russian).T. Bartoszynski, H. Judah, Set theory. On the structure of the Real Line, A.K. Peters, Wellesley 1995.Goffman, C., Neugebauer, C. J., & Nishiura, T. (1961). Density topology and approximate continuity. Duke Mathematical Journal, 28(4), 497-505. doi:10.1215/s0012-7094-61-02847-2E. Lazarow, The coarsest topology of I-approximately continuous functions, Comm. Math. Univ. Carolinae 27 (1986), 695-704.Oxtoby, J. C. (1980). Measure and Category. Graduate Texts in Mathematics. doi:10.1007/978-1-4684-9339-9W. Poreda, E. Wagner-Bojakowska, The topology of I-approximately continuous functions, Radovi Mat. 2 (1986), 263-277.W. Poreda, E. Wagner-Bojakowska, W. Wilczy_nski, A category analogue of the density topology Fund. Math. 125 (1985), 167-173.Tall, F. (1976). The density topology. Pacific Journal of Mathematics, 62(1), 275-284. doi:10.2140/pjm.1976.62.27

Carbon-dioxide emissions trading and hierarchical structure in worldwide finance and commodities markets

In a highly interdependent economic world, the nature of relationships between financial entities is becoming an increasingly important area of study. Recently, many studies have shown the usefulness of minimal spanning trees (MST) in extracting interactions between financial entities. Here, we propose a modified MST network whose metric distance is defined in terms of cross-correlation coefficient absolute values, enabling the connections between anticorrelated entities to manifest properly. We investigate 69 daily time series, comprising three types of financial assets: 28 stock market indicators, 21 currency futures, and 20 commodity futures. We show that though the resulting MST network evolves over time, the financial assets of similar type tend to have connections which are stable over time. In addition, we find a characteristic time lag between the volatility time series of the stock market indicators and those of the EU CO2 emission allowance (EUA) and crude oil futures (WTI). This time lag is given by the peak of the cross-correlation function of the volatility time series EUA (or WTI) with that of the stock market indicators, and is markedly different (>20 days) from 0, showing that the volatility of stock market indicators today can predict the volatility of EU emissions allowances and of crude oil in the near future.Comment: 4 figure

On topological properties of Fréchet locally convex spaces

[EN] We describe the topology of any cosmic space and any N-o-space in terms of special bases defined by partially ordered sets. Using this description we show that a Baire cosmic group is metrizable. Next, we study those locally convex spaces (lcs) E which under the weak topology sigma(E, E') are N-o-spaces. For a metrizable and complete lcs E not containing (an isomorphic copy of) l(1) and satisfying the Heinrich density condition we prove that (E, sigma(E,E')) is an N-o-space if and only if the strong dual of E is separable. In particular, if a Banach space E does not contain l(1), then (E, sigma(E, E')) is an N-o-space if and only if E' is separable. The last part of the paper studies the question: Which spaces (E, sigma(E, E')) are N-o-spaces? We extend, among the others, Michael's results by showing: If E is a metrizable lcs or a (DF)-space whose strong dual E' is separable, then (E, sigma(E, E')) is an N-o-space. Supplementing an old result of Corson we show that, for a Cech-complete Lindelof space X the following are equivalent: (a) X is Polish, (b) C-c(X) is cosmic in the weak topology, (c) the weak*-dual of C-c(X) is an N-o-space.The second and fourth named authors were supported by Generalitat Valenciana, Conselleria d'Educacio, Cultura i Esport, Spain, Grant PROMETEO/2013/058.Gabriyelyan, S.; Kakol, JM.; Kubzdela, A.; López Pellicer, M. (2015). On topological properties of Fréchet locally convex spaces. Topology and its Applications. 192(1):123-137. https://doi.org/10.1016/j.topol.2015.05.075S123137192