Characterization of Compact Sets by Their Dilation Volume

1995 ◽  
Vol 173 (1) ◽  
pp. 287-295 ◽  
Author(s):  
Jan Rataj
Keyword(s):  
Compact Sets

scholarly journals A New Characterization of Compact Sets in Fuzzy Number Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Huan Huang ◽  
Congxin Wu
Keyword(s):  
Fuzzy Number ◽  
Compact Sets ◽  
Sequential Compactness ◽  
Convergence Topology ◽  
Compact Subsets

We give a new characterization of compact subsets of the fuzzy number space equipped with the level convergence topology. Based on this, it is shown that compactness is equivalent to sequential compactness on the fuzzy number space endowed with the level convergence topology. Our results imply that some previous compactness criteria are wrong. A counterexample also is given to validate this judgment.

scholarly journals A Characterization for Compact Sets in the Space of Fuzzy Star-Shaped Numbers withLpMetric

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Zhitao Zhao ◽  
Congxin Wu
Keyword(s):  
Compact Sets ◽  
Compact Subsets

By means of some auxiliary lemmas, we obtain a characterization of compact subsets in the space of all fuzzy star-shaped numbers withLpmetric for1≤p<∞. The result further completes and develops the previous characterization of compact subsets given by Wu and Zhao in 2008.

scholarly journals Characterization of collectively compact sets of linear operators

1974 ◽  
Vol 55 (1) ◽  
pp. 45-54 ◽  
Author(s):  
John De Pree ◽  
Harry Klein
Keyword(s):  
Linear Operators ◽  
Compact Sets

scholarly journals Weak completeness of the Bourbaki quasi-uniformity

2001 ◽  
Vol 2 (1) ◽  
pp. 101 ◽  
Author(s):  
M.A. Sánchez Granero
Keyword(s):  
Uniform Space ◽  
Cluster Point ◽  
Compact Sets ◽  
Weak Completeness ◽  
Pseudometric Space

<p>The concept of semicompleteness (weaker than half-completeness) is defined for the Bourbaki quasi-uniformity of the hyperspace of a quasi-uniform space. It is proved that the Bourbaki quasi-uniformity is semicomplete in the space of nonempty sets of a quasi-uniform space (X,U) if and only if each stable filter on (X,U*) has a cluster point in (X,U). As a consequence the space of nonempty sets of a quasi-pseudometric space is semicomplete if and only if the space itself is half-complete. It is also given a characterization of semicompleteness of the space of nonempty U*-compact sets of a quasi-uniform space (X,U) which extends the well known Zenor-Morita theorem.</p>

Σ1 compactness for next admissible sets

1974 ◽  
Vol 39 (1) ◽  
pp. 105-116 ◽  
Author(s):  
Judy Green
Keyword(s):  
Compactness Theorem ◽  
Admissible Set ◽  
Compact Sets ◽  
Admissible Sets ◽  
New Class ◽  
Negative Results ◽  
Power Set ◽  
Consistency Property ◽  
Definition Of

Let σ be any sequence B0, B1 …, Bn, … of transitive sets closed under pairs with for each n. In this paper we show that the smallest admissible set Aσ with σ ∈ Aσ is Σ1 compact. Thus we have an entirely new class of explicitly describable uncountable Σ1 compact sets.The search for uncountable Σ1 compact languages goes back to Hanf's negative results on compact cardinals [7]. Barwise first showed that all countable admissible sets were Σ1 compact [1] and then went on to give a characterization of the Σ1 compact sets in terms of strict reflection [2]. While his characterization has been of interest in understanding the Σ1 compactness phenomenon it has led to the identification of only one class of uncountable Σ1 compact sets. In particular, Barwise showed [2], using the above notation, that if ⋃nBn is power set admissible it satisfies the strict reflection principle and hence is Σ1 compact. (This result was obtained independently by Karp using algebraic methods [9].)In proving our compactness theorem we follow Makkai's approach to the Barwise Compactness Theorem [12] and use a modified version of Smullyan's abstract consistency property [14]. A direct generalization of Makkai's method to the cofinality ω case yields a proof of the Barwise-Karp result mentioned above [6]. In order to obtain our new result we depart from the usual definition of language and use instead the indexed languages of Karp [9] in which a conjunction is considered to operate on a function whose range is a set of formulas rather than on a set of formulas itself.

A holomorphic characterization of compact sets in Banach spaces

2016 ◽  
Vol 47 (3) ◽  
pp. 863-869
Author(s):  
Humberto Carrión ◽  
Pablo Galindo ◽  
Mary Lilian Lourenço
Keyword(s):  
Banach Spaces ◽  
Compact Sets

A fixed-point characterization of weakly compact sets in L1(μ) spaces

2020 ◽  
Vol 491 (1) ◽  
pp. 124228
Author(s):  
Maria Japón ◽  
Chris Lennard ◽  
Roxana Popescu
Keyword(s):  
Fixed Point ◽  
Compact Sets ◽  
Weakly Compact ◽  
Weakly Compact Sets
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