Compact spaces representable as unions of nice subspaces

AbstractWe present several results on compact Hausdorff spaces which can be represented as unions of nice subspaces. Some typical results are: If X is a compact Hausdorff space, and X = ∪α<κXα, where each Xα is κ-refinable and Ψ(Xα) ⩽ κ, then (i) every nonempty Gκ-subset of X contains a point of character ⩽κ, (ii) if xϵX, χ(x, X) = μ > κ and μ is regular, then there exists a discrete sequence {xα: α<μ} in X such that xα→x, (iii) if A is a nonclosed subset of X, then there exists a point x ϵ X\A and a filter base F of subsets of A such that | F | ⩽κ and F→x. We also show that if a compact Hausdorff space X is a union of countably many metrizable spaces, X has no isolated points and c(X)=ω0, then X is a compactification of the space of irrationals

The Optical Gravitational Lensing Experiment. Variable Stars in Globular Clusters - IV. Fields 104A-E in 47 Tuc

Five fields located close to the center of the globular cluster NGC 104=47 Tuc were surveyed in a search for variable stars. We present V-band light curves for 42 variables. This sample includes 13 RR Lyr stars -- 12 of them belong to the Small Magellanic Cloud (SMC) and 1 is a background object from the galactic halo. Twelve eclipsing binaries were identified -- 9 contact systems and 3 detached/semi-detached systems. Seven eclipsing binaries are located in the blue straggler region on the cluster color-magnitude diagram (CMD) and four binaries can be considered main-sequence systems. One binary is probably a member of the SMC. Eight contact binaries are likely members of the cluster and one is most probably a foreground star. We show that for the surveyed region of 47 Tuc, the relative frequency of contact binaries is very low as compared with other recently surveyed globular clusters. The sample of identified variables also includes 15 red variables with periods ranging from about 2 days to several weeks. A large fraction of these 15 variables probably belong to the SMC but a few stars are likely to be red giants in 47 Tuc. VI photometry for about 50 000 stars from the cluster fields was obtained as a by product of our survey.Comment: Latex file, l-aa style, 10 pages, 7 ps figures included. Submitted to A&A. Figure 8 available from ftp://sirius.astrouw.edu.pl/pub/jka/47Tuc/fig8.ps.