On faint continuity

[EN] Recently the class of strongly faintly $\alpha$-continuous functions between topological spaces has been defined and studied in some detail. We consider this class of functions from the perspective of change(s) of topology. In particular, we conclude that each member of this class of functions belongs the usual class of continuous functions between topological spaces when the domain and codomain of the function in question have been retopologized appropriately. Some consequences of this fact are considered in this paper.Mccluskey, A.; Reilly, IL. (2015). On faint continuity. Applied General Topology. 16(1):45-52. doi:http://dx.doi.org/10.4995/agt.2015.3006.SWORD4552161D. Andrijevic, On b-open sets, Mat. Vesnik 48 (1996), 59-64.H. Corson and E. Michael, Metrizability of certain countable unions, Illinois J. Math. 8 (1964), 351-360.J. Dugundji, Topology, Allyn and Bacon, Boston, Mass. (1966).D. Gauld, M. Mrsevic, I. L. Reilly and M. K. Vamanamurthy, Continuity properties of functions, Coll. Math. Soc. Janos Bolyai 41 (1983), 311-322.Levine, N. (1963). Semi-Open Sets and Semi-Continuity in Topological Spaces. The American Mathematical Monthly, 70(1), 36. doi:10.2307/2312781P. E. Long and L. L. Herrington, Strongly $theta$-continuous functions, J. Korean Math. Soc. 18 (1981), 21-28.P. E. Long and L. L. Herrington, The $T_theta$-topology and faintly continuous functions, Kyungpook Math. J. 22 (1982), 7-14.S. N. Maheshwari and S. S. Thakur, On $alpha$-irresolute mappings, Tamkang J. Math. 11 (1980), 209-214.R. A. Mahmoud, M. E. Abd El-Monsef and A. A. Nasef, Some forms of strongly $mu$-continuous functions, $mu in alpha$-irresolute, open, closed, Kyungpook Math. J. 36 (1996), 143-150.A. S. Mashhour, M. E. Abd El-Monsef and S. N. El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Eygpt 53 (1982), 47-53.Nasef, A. A. (2009). Recent progress in the theory of faint continuity. Mathematical and Computer Modelling, 49(3-4), 536-541. doi:10.1016/j.mcm.2008.05.007A. A. Nasef and T. Noiri, Strong forms of faint continuity, Mem. Fac. Sci. Kochi Univ. Ser. A. Math. 19 (1998), 21-28.Njȧstad, O. (1965). On some classes of nearly open sets. Pacific Journal of Mathematics, 15(3), 961-970. doi:10.2140/pjm.1965.15.961T. Noiri, On $delta$-continuous functions, J. Korean Math. Soc. 16 (1980), 161-166.T. Noiri and V. Popa, Weak forms of faint continuity, Bull. Math. Soc. Sci. Math. R. S. Roumanie 34 (82) (1990), 263- 270.Reilly, I. L., & Vamanamurthy, M. K. (1985). On α-continuity in topological spaces. Acta Mathematica Hungarica, 45(1-2), 27-32. doi:10.1007/bf01955019Veličko, N. V. (1968). -closed topological spaces. Eleven Papers on Topology, 103-118. doi:10.1090/trans2/078/0

Star formation across cosmic time with radio surveys. The promise of the SKA

This lecture briefly reviews the major recent advances in radio astronomy made possible by ultra-deep surveys, reaching microJansky flux density levels. A giant step forward in many fields, including the study of the evolution of the cosmic star formation history is expected with the advent of the Square Kilometer Array (SKA).Comment: 28 pages, 3 figures, to be published in the Proceedings of the 3rd Cosmology School in Cracow, July 201

The Galactic disk mass-budget : II. Brown dwarf mass-function and density

In this paper, we extend the calculations conducted previously in the stellar regime to determine the brown dwarf IMF in the Galactic disk. We perform Monte Carlo calculations taking into account the brown dwarf formation rate, spatial distribution and binary fraction. Comparison with existing surveys seems to exclude a power-law MF as steep as the one determined in the stellar regime below 1 \msol and tends to favor a more flatish behaviour. Comparison with methane-dwarf detections tends to favor an eventually decreasing form like the lognormal or the more general exponential distributions determined in the previous paper. We calculate predicting brown dwarf counts in near-infrared color diagrams and brown dwarf discovery functions. These calculations yield the presently most accurate determination of the brown dwarf census in the Galactic disk. The brown dwarf number density is comparable to the stellar one, $n_{BD}\simeq n_\star\simeq 0.1$ pc$^{-3}$. The corresponding brown dwarf mass density, however, represents only about 10% of the stellar contribution, i.e. \rho_{BD}\simle 5.0\times 10^{-3} \mvol. Adding up the local stellar density determined previously yields the density of star-like objects, stars and brown dwarfs, in the solar neighborhood \rho_\odot \approx 5.0\times 10^{-2} \mvol.Comment: 39 pages, Latex file, uses aasms4.sty, to be published in ApJ, corrected version with correct figure

Far-Ultraviolet Radiation from Elliptical Galaxies

Far-ultraviolet radiation is a ubiquitous, if unanticipated, phenomenon in elliptical galaxies and early-type spiral bulges. It is the most variable photometric feature associated with old stellar populations. Recent observational and theoretical evidence shows that it is produced mainly by low-mass, small-envelope, helium-burning stars in extreme horizontal branch and subsequent phases of evolution. These are probably descendents of the dominant, metal rich population of the galaxies. Their lifetime UV outputs are remarkably sensitive to their physical properties and hence to the age and the helium and metal abundances of their parents. UV spectra are therefore exceptionally promising diagnostics of old stellar populations, although their calibration requires a much improved understanding of giant branch mass loss, helium enrichment, and atmospheric diffusion.Comment: 46 pages; includes LaTeX text file, 9 PS figures, 1 JPG figure, 2 style files. Full resolution figures and PS version available at http://www.astro.virginia.edu/~rwo/araa99/. Article to appear in Annual Reviews of Astronomy & Astrophysics, 199

A review of elliptical and disc galaxy structure, and modern scaling laws

A century ago, in 1911 and 1913, Plummer and then Reynolds introduced their models to describe the radial distribution of stars in `nebulae'. This article reviews the progress since then, providing both an historical perspective and a contemporary review of the stellar structure of bulges, discs and elliptical galaxies. The quantification of galaxy nuclei, such as central mass deficits and excess nuclear light, plus the structure of dark matter halos and cD galaxy envelopes, are discussed. Issues pertaining to spiral galaxies including dust, bulge-to-disc ratios, bulgeless galaxies, bars and the identification of pseudobulges are also reviewed. An array of modern scaling relations involving sizes, luminosities, surface brightnesses and stellar concentrations are presented, many of which are shown to be curved. These 'redshift zero' relations not only quantify the behavior and nature of galaxies in the Universe today, but are the modern benchmark for evolutionary studies of galaxies, whether based on observations, N-body-simulations or semi-analytical modelling. For example, it is shown that some of the recently discovered compact elliptical galaxies at 1.5 < z < 2.5 may be the bulges of modern disc galaxies.Comment: Condensed version (due to Contract) of an invited review article to appear in "Planets, Stars and Stellar Systems"(www.springer.com/astronomy/book/978-90-481-8818-5). 500+ references incl. many somewhat forgotten, pioneer papers. Original submission to Springer: 07-June-201