Displaying similar documents to “Sequential retractivities and regularity on inductive limits”

Sequential completeness of subspaces of products of two cardinals

Roman Frič, Nobuyuki Kemoto (1999)

Czechoslovak Mathematical Journal

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Let κ be a cardinal number with the usual order topology. We prove that all subspaces of κ 2 are weakly sequentially complete and, as a corollary, all subspaces of ω 1 2 are sequentially complete. Moreover we show that a subspace of ( ω 1 + 1 ) 2 need not be sequentially complete, but note that X = A × B is sequentially complete whenever A and B are subspaces of κ .

On FU( p )-spaces and p -sequential spaces

Salvador García-Ferreira (1991)

Commentationes Mathematicae Universitatis Carolinae

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Following Kombarov we say that X is p -sequential, for p ∈ α * , if for every non-closed subset A of X there is f ∈ α X such that f ( α ) ⊆ A and f ¯ ( p ) ∈ X ∖ A . This suggests the following definition due to Comfort and Savchenko, independently: X is a FU( p )-space if for every A ⊆ X and every x ∈ A - there is a function f ∈ α A such that f ¯ ( p ) = x . It is not hard to see that p ≤ RK q ( ≤ RK denotes the Rudin–Keisler order) ⇔ every p -sequential space is q -sequential ⇔ every FU( p )-space is a FU( q )-space. We generalize the spaces S n to construct examples of...

Sequential closures of σ -subalgebras for a vector measure

Werner J. Ricker (1996)

Commentationes Mathematicae Universitatis Carolinae

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Let X be a locally convex space, m : Σ → X be a vector measure defined on a σ -algebra Σ , and L 1 ( m ) be the associated (locally convex) space of m -integrable functions. Let Σ ( m ) denote { χ E ; E ∈ Σ } , equipped with the relative topology from L 1 ( m ) . For a subalgebra 𝒜 ⊆ Σ , let 𝒜 σ denote the generated σ -algebra and 𝒜 ¯ s denote the closure of χ ( 𝒜 ) = { χ E ; E ∈ 𝒜 } in L 1 ( m ) . Sets of the form 𝒜 ¯ s arise in criteria determining separability of L 1 ( m ) ; see [6]. We consider some natural questions concerning 𝒜 ¯ s and, in particular, its relation to χ ( 𝒜 σ ) . It is shown that...

On the global regularity of N -dimensional generalized Boussinesq system

Kazuo Yamazaki (2015)

Applications of Mathematics

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We study the N -dimensional Boussinesq system with dissipation and diffusion generalized in terms of fractional Laplacians. In particular, we show that given the critical dissipation, a solution pair remains smooth for all time even with zero diffusivity. In the supercritical case, we obtain component reduction results of regularity criteria and smallness conditions for the global regularity in dimensions two and three.

Pointwise regularity associated with function spaces and multifractal analysis

Stéphane Jaffard (2006)

Banach Center Publications

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The purpose of multifractal analysis of functions is to determine the Hausdorff dimensions of the sets of points where a function (or a distribution) f has a given pointwise regularity exponent H. This notion has many variants depending on the global hypotheses made on f; if f locally belongs to a Banach space E, then a family of pointwise regularity spaces C E α ( x ₀ ) are constructed, leading to a notion of pointwise regularity with respect to E; the case E = L ∞ corresponds to the usual Hölder regularity,...