Epimorphisms and maximal covers in categories of compact spaces

[EN] The category C is "projective complete"if each object has a projective cover (which is then a maximal cover). This property inherits from C to an epireflective full subcategory R provided the epimorphisms in R are also epi in C. When this condition fails, there still may be some maximal covers in R. The main point of this paper is illustration of this in compact Hausdorff spaces with a class of examples, each providing quite strange epimorphisms and maximal covers. These examples are then dualized to a category of algebras providing likewise strange monics and maximal essential extensions.Banaschewski, B.; Hager, A. (2013). Epimorphisms and maximal covers in categories of compact spaces. Applied General Topology. 14(1):41-52. doi:10.4995/agt.2013.1616.SWORD4152141H. Cook, Continua which admit only the identity mapping onto non-degenerate subcontinua, Fund. Math. 60 (1966) 214–249.R. Engelking, General Topology, Heldermann 1989.A. Gleason, Projective topological spaces, Ill. J. Math. 2 (1958), 482–489.L. Gillman and M. Jerison, Rings of Continuous Functions, Springer-Verlag 1976.HAGER, A. W. (1989). Minimal Covers of Topological Spaces. Annals of the New York Academy of Sciences, 552(1 Papers on Gen), 44-59. doi:10.1111/j.1749-6632.1989.tb22385.xHager, A. W., & Martinez, J. (1998). Singular Archimedean lattice-ordered groups. Algebra Universalis, 40(2), 119-147. doi:10.1007/s000120050086A. Hager and L. Robertson, Representing and ringifying a Riesz space, Symp. Math. XXI (1977), 411–431.H. Herrlich and G. Strecker, Category Theory, Allyn and Bacon 1973.Kennison, J. F. (1965). Reflective functors in general topology and elsewhere. Transactions of the American Mathematical Society, 118, 303-303. doi:10.1090/s0002-9947-1965-0174611-9Porter, J. R., & Woods, R. G. (1988). Extensions and Absolutes of Hausdorff Spaces. doi:10.1007/978-1-4612-3712-9V. Trnková, Non-constant continuous mappings of metric or compact Hausdorff spaces, Comm. Math. Univ. Carol. 13 (1972), 283–295

Functorial uniformization of topological spaces

AbstractLet T be the forgetful functor from uniform spaces to completely regular topological spaces. We study T-sections, i.e. functors right inverse to T. We develop as tool the notion of spanning a T-section by a class of uniform spaces, and the order-dual notion of cospanning. Coarsest and finest uniform bireflectors and coreflectors associated with a T-section are characterized. Certain effects of the uniform completion reflector on a T-section are expressed in terms of the associated bireflectors

Ten-year cardiovascular risk assessment in university students

Cardiovascular disease (CVD) is responsible for more than half of all deaths in the European region. The aim of the study was to compare body composition, blood pressure, total cholesterol (TC) and high density lipoprotein cholesterol (HDL-C), family history, activity behaviors, and the 10-year risk of having a heart attack between 166 university students (21.62 - 2.59 yrs) from Utah (USA) and 198 students (22.11 - 2.51 yrs) from Hungary. Ninety-two percent of the Hungarian students and 100% of the Utah students had an estimated 10-year Framingham risk score of 1% or less. The high prevalence of low risk was primarily due to the young age of study participants, healthy body composition and non-smoking behavior. Hungarians who had higher 10-year risk of heart attack had significantly higher waist hip ratio (WHR), TC, diastolic blood pressure (DBP) and were smokers compared to those Hungarians with lower risk. The self-reported physical activity levels between the two groups of students were not different. In conclusion the young men and women who participated in this study were, for the most part healthy; however the smoking habits and the lower physical activity of the Hungarian students likely elevated their risk of CVD.Scopu

On realcompact topological vector spaces

[EN] This survey paper collects some of older and quite new concepts and results from descriptive set topology applied to study certain infinite-dimensional topological vector spaces appearing in Functional Analysis, including Frechet spaces, (L F)-spaces, and their duals, (D F)-spaces and spaces of continuous real-valued functions C(X) on a completely regular Hausdorff space X. Especially (L F)-spaces and their duals arise in many fields of Functional Analysis and its applications, for example in Distributions Theory, Differential Equations and Complex Analysis. The concept of a realcompact topological space, although originally introduced and studied in General Topology, has been also studied because of very concrete applications in Linear Functional Analysis.The research for the first named author was (partially) supported by Ministry of Science and Higher Education, Poland, Grant no. NN201 2740 33 and for the both authors by the project MTM2008-01502 of the Spanish Ministry of Science and Innovation.Kakol, JM.; López Pellicer, M. (2011). On realcompact topological vector spaces. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas. 105(1):39-70. https://doi.org/10.1007/s13398-011-0003-0S39701051Argyros S., Mercourakis S.: On weakly Lindelöf Banach spaces. Rocky Mountain J. Math. 23(2), 395–446 (1993). doi: 10.1216/rmjm/1181072569Arkhangel’skii, A. V.: Topological Function Spaces, Mathematics and its Applications, vol. 78, Kluwer, Dordrecht (1992)Batt J., Hiermeyer W.: On compactness in L p (μ, X) in the weak topology and in the topology σ(L p (μ, X), L p (μ,X′)). Math. Z. 182, 409–423 (1983)Baumgartner J.E., van Douwen E.K.: Strong realcompactness and weakly measurable cardinals. Topol. 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Math. Soc. 79(1), 31–35 (2009). doi: 10.1017/S0004972708000968Ferrando J.C.: Some characterization for υ X to be Lindelöf Σ or K-analytic in term of C p (X). Topol. Appl. 156(4), 823–830 (2009). doi: 10.1016/j.topol.2008.10.016Ferrando J.C., Ka̧kol J.: A note on spaces C p (X) K-analytic-framed in $${\mathbb{R}^{X} }$$ . Bull. Aust. Math. Soc. 78, 141–146 (2008)Ferrando J.C., Ka̧kol J., López-Pellicer M.: Bounded tightness conditions and spaces C(X). J. Math. Anal. Appl. 297, 518–526 (2004)Ferrando J.C., Ka̧kol J., López-Pellicer M.: A characterization of trans-separable spaces. Bull. Belg. Math. Soc. Simon Stevin 14, 493–498 (2007)Ferrando, J.C., Ka̧kol, J., López-Pellicer, M.: Metrizability of precompact sets: an elementary proof. Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A. Mat. RACSAM 99(2), 135–142 (2005). http://www.rac.es/ficheros/doc/00173.pdfFerrando J.C., Ka̧kol J., López-Pellicer M., Saxon S.A.: Tightness and distinguished Fréchet spaces. J. Math. Anal. Appl. 324, 862–881 (2006). doi: 10.1016/j.jmaa.2005.12.059Ferrando J.C., Ka̧kol J., López-Pellicer M., Saxon S.A.: Quasi-Suslin weak duals. J. Math. Anal. Appl. 339(2), 1253–1263 (2008). doi: 10.1016/j.jmaa.2007.07.081Floret, K.: Weakly compact sets. Lecture Notes in Mathematics, vol. 801, Springer, Berlin (1980)Gillman L., Henriksen M.: Rings of continuous functions in which every finitely generated ideal is principial. Trans. Am. Math. Soc. 82, 366–391 (1956). doi: 10.2307/1993054Gillman L., Jerison M.: Rings of Continuous Functions. Van Nostrand Reinhold Company, New York (1960)Grothendieck A.: Sur les applications linéaires faiblement compactes d’espaces du type C(K). Can. J. Math. 5, 129–173 (1953)Gullick D., Schmets J.: Separability and semi-norm separability for spaces of bounded continuous functions. Bull. R. Sci. Lige 41, 254–260 (1972)Hager A.W.: Some nearly fine uniform spaces. Proc. Lond. Math. Soc. 28, 517–546 (1974). doi: 10.1112/plms/s3-28.3.517Howes N.R.: On completeness. Pacific J. Math. 38, 431–440 (1971)Isbell, J.R.: Uniform spaces. In: Mathematical Surveys 12, American Mathematical Society, Providence (1964)Ka̧kol J., López-Pellicer M.: Compact coverings for Baire locally convex spaces. J. Math. Anal. Appl. 332, 965–974 (2007). doi: 10.1016/j.jmaa.2006.10.045Ka̧kol, J., López-Pellicer, M.: A characterization of Lindelöf Σ-spaces υ X (preprint)Ka̧kol J., López-Pellicer M., Śliwa W.: Weakly K-analytic spaces and the three-space property for analyticity. J. Math. Anal. Appl. 362(1), 90–99 (2010). doi: 10.1016/j.jmaa.2009.09.026Ka̧kol J., Saxon S.: Montel (DF)-spaces, sequential (LM)-spaces and the strongest locally convex topology. J. Lond. Math. Soc. 66(2), 388–406 (2002)Ka̧kol J., Saxon S., Todd A.T.: Pseudocompact spaces X and df-spaces C c (X). Proc. Am. Math. Soc. 132, 1703–1712 (2004)Ka̧kol J., Śliwa W.: Strongly Hewitt spaces. 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Complut. 2(Supplementary Issue), 179–199 (1989)Pérez Carreras P., Bonet J.: Barrelled Locally Convex Spaces, Mathematics Studies 131. North-Holland, Amsterdam (1987)Pfister H.H.: Bemerkungen zum Satz über die separabilität der Fréchet-Montel Raüme. Arch. Math. (Basel) 27, 86–92 (1976). doi: 10.1007/BF01224645Robertson N.: The metrisability of precompact sets. Bull. Aust. Math. Soc. 43(1), 131–135 (1991). doi: 10.1017/S0004972700028847Rogers C.A., Jayne J.E., Dellacherie C., Topsøe F., Hoffman-Jørgensen J., Martin D.A., Kechris A.S., Stone A.H.: Analytic Sets. Academic Press, London (1980)Saxon S.A.: Nuclear and product spaces, Baire-like spaces, and the strongest locally convex topology. Math. Ann. 197(2), 87–106 (1972). doi: 10.1007/BF01419586Schawartz L.: Radom Measures on Arbitrary Topological Spaces and Cylindrical Measures. Oxford University Press, Oxford (1973)Schlüchtermann G., Wheller R.F.: On strongly WCG Banach spaces. Math. 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Springer, Berlin (1974

Algebraic properties of the uniform closure of spaces of continuous functions

For a completely regular space X, C(X) denotes the algebra of all real-valued and continuous functions over X. This paper deals with the problem of knowing when the uniform closure of certain subsets of C(X) has certain algebraic properties. In this context we give an internal condition, “property A,” to characterize the linear subspaces whose uniform closure is an inverse-closed subring of C(X)

Kinetic simulations of scrape-off layer physics in the DIII-D tokamak

Simulations using the fully kinetic code XGCa were undertaken to explore the impact of kinetic effects on scrape-off layer (SOL) physics in DIII-D H-mode plasmas. XGCa is a total-f, gyrokinetic code which self-consistently calculates the axisymmetric electrostatic potential and plasma dynamics, and includes modules for Monte Carlo neutral transport. Fluid simulations are normally used to simulate the SOL, due to its high collisionality. However, depending on plasma conditions, a number of discrepancies have been observed between experiment and leading SOL fluid codes (e.g. SOLPS), including underestimating outer target temperatures, radial electric field in the SOL, parallel ion SOL flows at the low field side, and impurity radiation. Many of these discrepancies may be linked to the fluid treatment, and might be resolved by including kinetic effects in SOL simulations.The XGCa simulation of the DIII-D tokamak in a nominally sheath-limited regime show many noteworthy features in the SOL. The density and ion temperature are higher at the low-field side, indicative of ion orbit loss. The SOL ion Mach flows are at experimentally relevant levels (Mi ∼ 0.5), with similar shapes and poloidal variation as observed in various tokamaks. Surprisingly, the ion Mach flows close to the sheath edge remain subsonic, in contrast to the typical fluid Bohm criterion requiring ion flows to be above sonic at the sheath edge. Related to this are the presence of elevated sheath potentials, eΔΦ/Te∼3−4, over most of the SOL, with regions in the near-SOL close to the separatrix having eΔΦ/Te > 4. These two results at the sheath edge are a consequence of non-Maxwellian features in the ions and electrons there