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Register a new userWhat makes a Stone topological algebra profinite
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This paper is a contribution to understanding what properties should a topological algebra on a Stone space satisfy to be profinite. We reformulate and simplify proofs for some known properties using syntactic congruences. We also clarify the role of various alternative ways of describing syntactic congruences, namely by finite sets of terms and by compact sets of continuous self mappings of the algebra.
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The notions of a {em 2-precontact space}/ and a {em 2-contact space}/ are introduced. Using them, new representation theorems for precontact and contact algebras are proved. It is shown that there are bijective correspondences between such kinds of algebras and such kinds of spaces. As applications of the obtained results, we get new connect
We prove a new duality theorem for the category of precontact algebras which implies the Stone Duality Theorem, its connected version obtained in arXiv:1508.02220v3, 1-44 (to appear in Topology Appl.), the recent duality theorems of Bezhanishvili, G., Bezhanishvili, N., Sourabh, S., Venema, Y. and Goldblatt, R. and Grice, M, and some new duality theorems for the category of contact algebras and for the category of complete contact algebras.
We compare the Spectral Energy Distribution (SED) of radio-loud and radio-quiet AGNs in three different samples observed with SDSS: radio-loud AGNs (RLAGNs), Low Luminosity AGNs (LLAGNs) and AGNs in isolated galaxies (IG-AGNs). All these galaxies have similar optical spectral characteristics. The median SED of the RLAGNs is consistent with the characteristic SED of quasars, while that of the LLAGNs and IG-AGNs are consistent with the SED of LINERs, with a lower luminosity in the IG-AGNs than in the LLAGNs. We infer the masses of the black holes (BHs) from the bulge masses. These increase from the IG-AGNs to the LLAGNs and are highest for the RLAGNs. All these AGNs show accretion rates near or slightly below 10% of the Eddington limit, the differences in luminosity being solely due to different BH masses. Our results suggests there are two types of AGNs, radio quiet and radio loud, differing only by the mass of their bulges or BHs.
We view a complex liquid as a network of bonds connecting each particle to its nearest neighbors; the dynamics of this network is a chain of discrete events signaling particles rearrangements. Within this picture, we studied a two-dimensional complex liquid and found a stretched-exponential decay of the network memory and a power-law for the distribution of the times for which a particle keeps its nearest neighbors; the dependence of this distribution on temperature suggests a possible dynamical critical point. We identified and quantified the underlying spatio-temporal phenomena. The equilibrium liquid represents a hierarchical structure, a mosaic of long-living crystallites partially separated by less-ordered regions. The long-time dynamics of this structure is dominated by particles redistribution between dynamically and structurally different regions. We argue that these are generic features of locally ordered but globally disordered complex systems. In particular, these features must be taken into account by any coarse-grained theory of dynamics of complex fluids and glasses.
We construct Menger subsets of the real line whose product is not Menger in the plane. In contrast to earlier constructions, our approach is purely combinatorial. The set theoretic hypothesis used in our construction is far milder than earlier ones, and holds in all but the most exotic models of real set theory. On the other hand, we establish productive properties f
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