MAT 578 Functional Analysis
نویسنده
چکیده
Proof. The first statement is obvious since every intersection of closed sets is closed and every intersection of convex sets is convex. For the second statement, let C = coA. first note that coA ⊂ coA since coA is convex and contains A. Thus C ⊂ coA since coA is closed. On the other hand, if we knew that C were convex then it would be a closed convex set containing A, hence would contain coA, and we would done. So, it now suffices to verify the general fact that the closure of any convex set B is convex: let x, y ∈ B and 0 < t < 1. Choose xi, yi ∈ B such that xi → x and yi → y. Then (1− t)xi + tyi → (1− t)x + ty, so (1− t)x + ty ∈ B since (1− t)xi + tyi ∈ B for all i.
منابع مشابه
Switching of a mating-type a mutant allele in budding yeast Saccharomyces cerevisiae.
Aimed at investigating the recovery of a specific mutant allele of the mating type locus (MAT) by switching a defective MAT allele, these experiments provide information bearing on several models proposed for MAT interconversion in bakers yeast, Saccharomyces cerevisiae. Hybrids between heterothallic (ho) cells carrying a mutant MAT a allele, designated mata-2, and MAT alpha ho strains show a h...
متن کاملApplication of Numerical Methods in the Analysis of Mat Foundations and Limitations of Classical Methods
متن کامل
Application of Numerical Methods in the Analysis of Mat Foundations and Limitations of Classical Methods
متن کامل
Complete genetic linkage maps from an interspecific cross between Fusarium circinatum and Fusarium subglutinans.
The Gibberella fujikuroi complex includes many plant pathogens of agricultural crops and trees, all of which have anamorphs assigned to the genus Fusarium. In this study, an interspecific hybrid cross between Gibberella circinata and Gibberella subglutinans was used to compile a genetic linkage map. A framework map was constructed using a total of 578 AFLP markers together with the mating type ...
متن کاملGenetic variance in the composition of two functional groups (diazotrophs and cyanobacteria) from a hypersaline microbial mat.
Examination of variation in ecological communities can lead to an understanding of the forces that structure communities, the consequences of change at the ecosystem level, and the relevant scales involved. This study details spatial and seasonal variability in the composition of nitrogen-fixing and cyanobacterial (i.e., oxygenic photosynthetic) functional groups of a benthic, hypersaline micro...
متن کامل