La normalidad de un espacio topológico no es una propiedad local

M . Valdivia and M. López have obtained in (4) and (3) completely regular topological spaces whose associated k-spaces are not regular. Here we prove that these k-spaces are such that every point admits a neighbourhood which, endowed with the induced topology, is normal

Webs and Bounded Finitely Additive Measures

AbstractLetM={μs:s∈S} be a family of scalar bounded finitely additive measures defined on a σ-algebra A. The Nikodym–Grothendieck boundedness theorem states that ifMis simply bounded in A thenMis uniformly bounded in A. In this paper we prove that if V={Ascr;n1,n2,…,np:p,n1,n2…np∈N} is an increasing web in A, then there is a strand {An1n2…ni:i∈N} such that ifMis simply bounded in one An1n2…nithenMis uniformly bounded in A (Theorem 3.1). This result is deduced from the fact that if W={En1n2…np:p,n1,n2,…,np∈N} is a linear increasing web inl0∞(X,A), then there exists a strand {En1n2…ni:i∈N} such that everyEn1n2…niis barrelled and dense inl0∞(X,A) (Theorem 2.7). From this strong barrelledness condition previous results of the author jointly with J. C. Ferrando are improved here. These results are related to the classical result of Diestel and Faires in vector measures

Weak Sequential Convergence in Bounded Finitely Additive Measures

[EN] It is well known that a ¿-algebra ¿ of subsets of a set ¿ verifies both Nikodým property and property (G) for the Banach space ba(¿) of bounded finitely additive measures defined in ¿. A classic result of Valdivia stating that if a ¿-algebra ¿ is covered by an increasing sequence (¿n:n¿N) of subsets, there is p¿N such that ¿p is a Nikodým set for ba(¿) was complemented in Ferrando et al. (2020) proving that there exists p¿N such that ¿p is both a Nikodým and a Grothendieck set for ba(¿). Valdivia result was the first step to get that if (¿¿:¿¿N<¿) is a web in ¿ there exists a chain (¿n:n¿N) in N<¿ such that each ¿¿n, n¿N, is a Nikodým set for ba(¿). In this paper, we develop several properties in Banach spaces that enables us to complement the preceding web result extending the main result in Ferrando et al. (2020) proving that for each web (¿¿:¿¿N<¿) in a ¿-algebra ¿ there exists a chain (¿n:n¿N) in N<¿ such that each ¿¿n, n¿N, is both a Nikodým and a Grothendieck set for ba(¿). As an application we extend some results of classic Banach space theoryThe second author is supported by Grant PGC2018-094431-B-I00 of the Ministry of Science, Innovation and Universities of Spain.López Alfonso, S.; López Pellicer, M. (2020). Weak Sequential Convergence in Bounded Finitely Additive Measures. Vietnam Journal of Mathematics. 48(2):379-389. https://doi.org/10.1007/s10013-020-00387-2S379389482Arens, R.F., Kelley, J.L.: Characterizations of the space of continuous functions over a compact Hausdorff space. Trans. Am. Math. Soc. 62, 499–508 (1947)Diestel, J., Faires, B., Huff, R.: Convergence and boundedness of measures in non σ-complete algebras. Preprint (1976)Diestel, J., Uhl, J.J.: Vector Measures. Mathematical Surveys and Monographs, vol. 15. American Mathematical Society, Providence (1977)Dunford, N., Schwartz, J.T.: Linear Operators. Part I: General Theory. Wiley, New Jersey (1988)Fernández, J., Hui, S., Shapiro, H.: Unimodular functions and uniform boundedness. Publ. Mat. 33, 139–146 (1989)Ferrando, J.C., Ka̧kol, J., López-Pellicer, M.: On spaces Cb(X) weakly K-analytic. Math. Nachr. 290, 2612–2618 (2017)Ferrando, J.C., López-Alfonso, S., López-Pellicer, M.: On Nikodým and Rainwater sets for $ba(\mathcal {R})$ and a problem of M. Valdivia. Filomat 33, 2409–2416 (2019)Ferrando, J.C., López-Alfonso, S., López-Pellicer, M.: On the Grothendieck property (submited) (2020)Ferrando, J.C., López-Pellicer, M., Sánchez Ruiz, L.M.: Metrizable Barrelled Spaces. Pitman Research Notes in Mathematics Series, vol. 332. Longman, Harlow (1995)Ferrando, J.C., Sánchez Ruiz, L.M.: A survey on recent advances on the Nikodým boundedness theorem and spaces of simple functions. Rocky Mount. J. Math. 34, 139–172 (2004)Fonf, V.P.: On exposed and smooth points of convex bodies in Banach spaces. Bull. Lond. Math. Soc. 28, 51–58 (1996)Ka̧kol, J., López-Pellicer, M.: On Valdivia strong version of Nikodým boundedness property. J. Math. Anal. Appl. 446, 1–17 (2017)López-Alfonso, S., Mas, J., Moll, S.: Nikodým boundedness property and webs in σ-algebras. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM 110, 711–722 (2016)López-Alfonso, S.: On Schachermayer and Valdivia results in algebras of Jordan measurable sets. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 110, 799–808 (2016)López-Pellicer, M.: Webs and bounded finitely additive measures. J. Math. Anal. Appl. 210, 257–267 (1997)Nygaard, O.: A strong uniform boundedness principle in Banach spaces. Proc. Am. Math. Soc. 129, 861–863 (2001)Nygaard, O.: Thick sets in Banach spaces and their properties. Quaest. Math. 29, 50–72 (2006)Plebanek, G., Sobota, D.: Countable tightness in the spaces of regular probability measures. Fund. Math. 229, 159–170 (2015)Rainwater, J.: Short notes: Weak convergence of bounded sequences. Proc. Am. Math. Soc. 14, 999–999 (1963)Schachermayer, W.: On some classical measure-theoretic theorems for non-sigma-complete Boolean algebras. Diss. Math. (Rozprawy Mat.) 214, 1–33 (1982)Simons, S.: A convergence theorem with boundary. Pac. J. Math. 40, 703–708 (1972)Sobota, D., Zdomskyy, L.: The Nikodým property in the Sacks model. Topol. Appl. 230, 24–34 (2017)Talagrand, M.: Propriété de Nikodým and propriété de Grothendieck. Stud. Math. 78, 165–171 (1984)Valdivia, M.: On certain barrelled normed spaces. Ann. Inst. Fourier 29, 39–56 (1979)Valdivia, M.: On Nikodým boundedness property. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 107, 355–372 (2013

On Valdivia strong version of Nikodym boundedness property

[EN] Following Schachermayer, a subset B of an algebra A of subsets of &#937; is said to have the N-property if a B-pointwise bounded subset Mof ba(A)is uniformly bounded on A, where ba(A) is the Banach space of the real (or complex) finitely additive measures of bounded variation defined on A. Moreover B is said to have the strong N-property if for each increasing countable covering (B_m)_m of B there exists B_n which has the N-property. The classical Nikodym Grothendieck s theorem says that each &#963;-algebra S of subsets of &#937; has the N-property. The Valdivia s theorem stating that each &#963;-algebra S has the strong N-property motivated the main measure-theoretic result of this paper: We show that if (B_{m_1})_{m_1} is an increasing countable covering of a &#963;-algebra S and if (B_{m_1},_{m_2},...,_{m_p}_{m_(p+1)}}_{m_(p+1)} is an increasing countable covering of B_{m_1},_{m_2},...,_{m_p}, for each p, m_i \in N, 1 less than or equal i less than or equal p, then there exists a sequence (n_i)_i such that each B_{n_1},_{n_2},...,_{n_r}, r&#8712;N, has the strong N-property. In particular, for each increasing countable covering (B_m)_m of a &#963;-algebra S there exists B_n which has the strong N-property, improving mentioned Valdivia s theorem. Some applications to localization of bounded additive vector measures are provided.This research was supported for the first named author by the GACR project 16-34860L and RVO: 67985840. It was also supported 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. (2017). On Valdivia strong version of Nikodym boundedness property. Journal of Mathematical Analysis and Applications. 446(1):1-17. doi:10.1016/j.jmaa.2016.08.032S117446

Pulsed light inactivation of mushroom polyphenol oxidase: a fluorometric and spectrophotometric study

Polyphenol oxidase (PPO) is one of the most important food enzymes, it is responsible for the browning of many foods. Pulsed light (PL) is a non-thermal method of food preservation that is able to inactivate PPO. The aim of this work was to gain insight into the mechanism of PPO inactivation by PL. To this, the kinetics of PPO inactivation by PL was measured, together with associated changes in tryptophan fluorescence, KI fluorescence quenching and turbidity; and results were analysed by parameter A and phase diagram methods. Enzyme inactivation followed the Weibull model. Tryptophan fluorescence decreased during PL treatment, as well as the parameter A, while Stern-Volmer constants increased and turbidity was constant. The phase diagram showed only two populated states. There was a high correlation between the loss of activity and parameter A. Results indicate that under the experimental conditions, the inactivation of PPO by PL is an all-or-none process where the enzyme progressively unfolds with no evidence of aggregation.Fundación Universitaria San Antonio de CartagenaCiencias de la Alimentació

Classifying Topologies through G-Bases

[EN] We classify several topological properties of a Tychonoff space $X$ by means of certain locally convex topologies $\mathcal{T}$ with a $\mathfrak{G}$-base located between the pointwise topology $\tau _{p}$ and the bounded-open topology $\tau _{b}$ of the real-valued continuous function space $C\left( X\right)$.This research was funded in part by grant PGC2018-094431-B-I00 of Ministry of Science, Innovation and Universities of Spain.Ferrando, JC.; López Pellicer, M. (2022). Classifying Topologies through G-Bases. Axioms. 11(12):1-7. https://doi.org/10.3390/axioms1112074417111

Covering Properties of Cp(X) and Ck(X)

[EN] Let X be a Tychonoff space. We survey some classic and recent results that characterize the topology or cardinality of X when C-p (X) or C-k (X) is covered by certain families of sets (sequences, resolutions, closure-preserving coverings, compact coverings ordered by a second countable space) which swallow or not some classes of sets (compact sets, functionally bounded sets, pointwise bounded sets) in C(X).Research supported by Grant PGC2018-094431-B-I00 of Ministry of Science, Innovation & Universities of Spain.Ferrando, JC.; López Pellicer, M. (2020). Covering Properties of Cp(X) and Ck(X). Filomat. 34(11):3575-3599. https://doi.org/10.2298/FIL2011575FS35753599341

Oriente y Occidente en la Formación de la Ciencia

V PROGRAMA DE PROMOCIÓN DE LA CULTURA CIENTÍFICA Y TECNOLÓGICA[ES] Hay científicos propensos a creer que casi todas las cosas de algún valor se hicieron en los dos últimos siglos, debido a los resultados asombrosos obtenidos en tiempos recientes, y que nadie cuestiona que se apoyan en la labor preparatoria de los esfuerzos anteriores. Aún admitiendo que los resultados del presente sean más complejos y más valiosos que los del pasado, y que los han reemplazado, el pensamiento inductivo nos hace suponer que serán reemplazados por los resultados del futuro. Por tanto, la historia de la ciencia siempre ha proporcionado en cada época una visión menos presuntuosa de su participación en la evolución humana.Tanto para entender al hombre a través del desarrollo de la civilización, como para la comprensión del significado más profundo de la ciencia se necesita la historia de la ciencia, siendo la historia antigua y medieval tan útil como la moderna. El análisis de la contribución de oriente y occidente en la formación de la ciencia nos obliga a mirar hacia la historia antigua y medievalLópez Pellicer, M. (2005). Oriente y Occidente en la Formación de la Ciencia. REAL ACADEMIA DE CIENCIAS EXACTAS, FISICAS Y NATURALES. 99(1):1-26. http://hdl.handle.net/10251/76812S12699

Recuerdo de Julio Rey Pastor

[ES] Se describe: 1. La actividad Matemática española a mediados del XIX 2. El Premio Nobel de Santiago Ramón y Cajal y la Junta para la Amplliación de Estudios. 3. La época de estudiante de Rey Pastor. 4. La fundación de la REal Sociedad Matemática Española. 5. Rey Pastor catedrático en las Universidades de Oviedo y en la Universidad Central. 6. Rey Pastor en Argentina. 7. El ingreso de Rey Pastor en la Real Academia de Ciencias. 8. La influencia de Rey Pastor en la escuela matemática argentina. 9. La influencia internacional de Rey Pastor. 10. Sus contribuciones al regresar a España (el Instituto de Cálcculo, la fundación de la Sociedad Española de Matemática Aplicada y el Semianrio de Historia de la Ciencia). 11. Su ingreso en la Real Academia Española. 12. Resumen de su obra.López Pellicer, M. (2015). Recuerdo de Julio Rey Pastor. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. 108(1):55-72. http://hdl.handle.net/10251/99733S5572108

In memoriam: Manuel Valdivia Ureña (1928-2014)

El artículo está dividido en 9 secciones. En la primera sección se describe el camino del profesor Valdivia hacia la Matemática, pues primero estudió Ingeniería Agronómica. Las siete secciones siguientes describen algunos de los temas en que el profesor Valdivia obtuvo resultados significativos (2. El teorema General de la Gráfica Cerrada;3. Espacios de Pták; 4. Soluciones de Valdivia a problemas de Grothendieck y Schwartz; 5. Otros resultados de Valdivia sobre espacios localmente convexos; 6. Algunos resultados de Valdivia sobre espacios de Banach; 7. Holomorfía infinita, espacios de polinomios y formas multilineales; 8. Desarrollos asintóticos y analiticidad real). La última sección se dedica a esbozar algunas cualidades de Valdivia como profesor y maestro, Este artículo no abarca toda la obra del profesor Valdivia, pues en las referencias solo se citan 99 de los 192 artículos del profesor Valdivia que figuran en la base de datos MathSciNet ( http://www.ams.org/mathscinet/search/author.html?mrauthid=176625 ).López Pellicer, M. (2014). In memoriam: Manuel Valdivia Ureña (1928-2014). Gaceta de la Real Sociedad Matemática Española. 17(3):455-484. http://hdl.handle.net/10251/74411S45548417