In this paper we prove that if κ is a cardinal in L[0], then there is an inner model M such that M |= (Vκ,∈) has no elementary end extension. In particular if 0♯ exists then weak compactness is never downwards absolute. We complement the result with a lemma stating that any cardinal greater than א1 of uncountable cofinality in L[0♯] is Mahlo in every strict inner model of L[0♯].

In this paper,  it is shown that the category of $L$-ordered fuzzifying convergence spaces contains the category of pretopological $L$-ordered fuzzifying convergence spaces as a bireflective subcategory and the latter contains the category of topological $L$-ordered fuzzifying convergence spaces as a bireflective subcategory. Also, it is proved that the category of $L$-ordered fuzzifying conver...

In this paper, as an application of fuzzy matroids, the fuzzifying greedy algorithm is proposed and an achievableexample is given. Basis axioms and circuit axioms of fuzzifying matroids, which are the semantic extension for thebasis axioms and circuit axioms of crisp matroids respectively, are presented. It is proved that a fuzzifying matroidis equivalent to a mapping which satisfies the basis ...

is precompact in the C1,α topology. Here R denotes the Riemann curvature tensor, vol the volume and diam the diameter of (M,g). Thus, for any sequence of metrics gi on n-manifolds Mi satisfying (1.1), there is a subsequence, also called gi, and diffeomorphisms φi : M∞ → Mi such that the metrics φi gi converge in the C 1,α topology to a limit metric g∞ onM∞, for any α < 1. In particular, there a...

These notes give a summary of results that everyone who does work in functional analysis should know about the weak topology on locally convex topological vector spaces and the weak-* topology on their dual spaces. The most striking of the results we prove is Theorem 9, which shows that a subset of a locally convex space is bounded if and only if it is weakly bounded. It is straightforward to p...

in this paper, the notion of maximal m-open set is introduced and itsproperties are investigated. some results about existence of maximal m-open setsare given. moreover, the relations between maximal m-open sets in an m-spaceand maximal open sets in the corresponding generated topology are considered.our results are supported by examples and counterexamples.

In functional analysis it is well known that every linear functional defined on the dual of a locally convex vector space which is continuous for the weak topology is the evaluation at a uniquely determined point of the given vector space. M. Schröder and A. Simpson have obtained a similar result for lower semicontinuous linear functionals on the cone of all Scott-continuous valuations on a top...

We discuss a little-studied class of weak decay modes sensitive to only one quark topology at leading order in GF : M → mγ, where M,m are mesons with completely distinct flavor quantum numbers. Specifically, they proceed via the annihilation of the valence quarks through a W and the emission of a single hard photon, and thus provide a clear separation between CKM and strong interaction physics....