Spaces $X$ in which all prime $z$-ideals of $C(X)$ are minimal or maximal

Melvin Henriksen; Jorge Martinez; Grant R. Woods

Best approximations and porous sets

Simeon Reich, Alexander J. Zaslavski (2003)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let $D$ be a nonempty compact subset of a Banach space $X$ and denote by $S (X)$ the family of all nonempty bounded closed convex subsets of $X$ . We endow $S (X)$ with the Hausdorff metric and show that there exists a set $ℱ \subset S (X)$ such that its complement $S (X) ∖ ℱ$ is $σ$ -porous and such that for each $A \in ℱ$ and each $\tilde{x} \in D$ , the set of solutions of the best approximation problem $∥ \tilde{x} - z ∥ \to min$ , $z \in A$ , is nonempty and compact, and each minimizing sequence has a convergent subsequence.

Some results on $L Σ (κ)$ -spaces

Fidel Casarrubias Segura, Oleg Okunev, Paniagua C. G. Ramírez (2008)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We present several results related to $L Σ (κ)$ -spaces where $κ$ is a finite cardinal or $ω$ ; we consider products and some constructions that lead from spaces of these classes to other spaces of similar classes.

Displaying similar documents to “Spaces X in which all prime z -ideals of C ( X ) are minimal or maximal”

Best approximations and porous sets

Some results on L Σ ( κ ) -spaces

Displaying similar documents to “Spaces $X$ in which all prime $z$ -ideals of $C (X)$ are minimal or maximal”

Some results on $L Σ (κ)$ -spaces