… of the closed unit ball is a relatively weakly open subset of the … convex combination of slices
C of the unit ball of a Banach space X and \(x\in C\), there exists a relatively weakly open set …

… nonempty relatively weakly open subset, respectively every convex combinations of slices,
… Also we define the weak-star versions of the above properties, the w ⁎ -slice-S2P, w ⁎ -D2P …

… Furthermore, x 0 is a convex combination of elements of A ⊂ K and so x 0 ∈ K . Finally, for
1 ≤ j ≤ n , one has e ø ⌢ j ⁎ ( x 0 ) = ∑ i = 1 i ≠ j n 1 n e ø ⌢ j ⁎ ( x ø ⌢ i ) + 1 n e ø ⌢ j ⁎ ( x ø …

… We show that c0 and, in fact, C(K) for any scattered compact Hausdorff space K have the
property that finite convex combinations of slices of the unit ball are relatively weakly open …

… all different from each other: every finite convex combination of slices of the unit ball is (1)
relatively weakly open, (2) has nonempty interior in relative weak topology of the unit ball, and (…

… | V strongly open in X… slice convergence of {f*Og* } evvThe dual upper slice topology is,
similarly, related to the upper Kuratowski convergence of epigraphs relative to the bounded-weak…

… We show that c0, and in fact C(K) for any scattered compact Hausdorff space K, have the
property that finite convex combinations of slices of the unit ball are relatively weakly open …

… property and the size of convex combinations of slices in Banach spaces. We … , and only if,
every convex combination of w ⁎ -slices in the dual unit ball has … Relatively weakly open sets …

… that finite convex combinations of slices of BC(K,K) are relatively weakly open in BC(K,K). …
that finite convex combinations of slices of BC0(K,X) are relatively weakly open in BC0(K,X). …

… convex combinations of slices of the unit ball are relatively open or have non-empty relative
… , we consider the analogous concept of convex combination of weak-star slices of \(B_X\). …