2. The Freudenthal theorem for symmetric spaces Our primary interest is in the classical compact groups; nevertheless, it is essential for our method to consider the larger family of compact symmetric spaces. A compact homogeneous Riemannian manifold M is called symmetric if it admits an 'inverse operation', i.e. if M admits an isometry, keeping a point P e M fixed, and whose differential at P ...

The mass-radius relation of compact stars is discussed with relation to the presence of quark matter in the core. The existence of a new family of compact stars with quark matter besides white dwarfs and ordinary neutron stars is outlined.

We proved that a finite commuting Boyd-Wong type contractive family with equicontinuous words have the approximate common fixed point property. We also proved that given X Ă R, compact and convex subset, F : X Ñ X a compact-and-convex valued Lipschitz correspondence and g an isometry on X, then gF “ F g implies F admits a Lipschitz selection commuting with g.

We prove that noncommutative solenoids are limits, in the sense of the Gromov-Hausdorff propinquity, of quantum tori. From this observation, we prove that noncommutative solenoids can be approximated by finite dimensional quantum compact metric spaces, and that they form a continuous family of quantum compact metric spaces over the space of multipliers of the solenoid, properly metrized.

We compare two institutions head on, a family compact – a parent makes a transfer to her parent in anticipation of a possible future gift from her children – with a pay-as-you-go, social security system in a lifecycle model with endogenous fertility wherein children are valued both as consumption and investment goods. Our focus is strictly on the pension dimension of these competing institution...

We prove that the cohomology groups of a definably compact set over an o-minimal expansion of a group are finitely generated and invariant under elementary extensions and expansions of the language. We also study the cohomology of the intersection of a definable decreasing family of definably compact sets, under the additional assumption that the o-minimal structure expands a field.

We give a geometric proof of the following well-established theorem for o-minimal expansions of the real field: the Hausdorff limits of a compact, definable family of sets are definable. While previous proofs of this fact relied on the model-theoretic compactness theorem, our proof explicitely describes the family of all Hausdorff limits in terms of the original family.

(a) X is said to be a Loeb space i® the family of all non-empty, closed subsets of X has a choice function. (b) X is said to be selective i® the family of all non-empty, open subsets of X has a choice function. (c) X is said to be locally compact i® each point in X has a neighborhood base consisting of compact sets. (d) X is called second countable if it has a countable base for T . (e) X is ca...

in this paper, countable compactness and the lindel¨of propertyare defined for l-fuzzy sets, where l is a complete de morgan algebra. theydon’t rely on the structure of the basis lattice l and no distributivity is requiredin l. a fuzzy compact l-set is countably compact and has the lindel¨ofproperty. an l-set having the lindel¨of property is countably compact if andonly if it is fuzzy compact. ...

We show that the property of sequential compactness for subspaces of R is countably productive in ZF. Also, in the language of weak choice principles, we give a list of characterizations of the topological statement ‘sequentially compact subspaces of R are compact’. Furthermore, we show that forms 152 (= every non-well-orderable set is the union of a pairwise disjoint well-orderable family of d...