On absolute retracts, P(S) and complemented subspaces of $C(D^{ω_{1}})$

On Contractively Complemented Subspaces

Abstract. It is shown that for an L1-predual space X and a countable linearly independent subset of ext(BX∗) whose norm-closed linear span Y in X∗ is w∗-closed, there exists a w∗-continuous contractive projection from X∗ onto Y . This result combined with those of Pelczynski and Bourgain yields a simple proof of the Lazar-Lindenstrauss theorem that every separable L1-predual with non-separable ...

On Retracts, Absolute Retracts, and Folds in Cographs

Let G and H be two cographs. We show that the problem to determine whether H is a retract of G is NP-complete. We show that this problem is fixed-parameter tractable when parameterized by the size of H. When restricted to the class of threshold graphs or to the class of trivially perfect graphs, the problem becomes tractable in polynomial time. The problem is also soluble in linear time when on...

On quasi-complemented subspaces of banach spaces.

On Local Connectedness of Absolute Retracts

One of the fundamental observations of theory of retracts says that any absolute retract for the class of all compacta is a locally connected continuum. However, when more restricted classes of spaces are considered, as for example hereditarily unicoherent continua, tree-like continua, dendroids, or hereditarily indecomposable continua, this is not necessarily the case (see e.g., [6, Corollarie...

PFA and complemented subspaces of ℓ∞/c0

The Banach space `∞/c0 is isomorphic to the linear space of continuous functions on N∗ with the supremum norm, C(N∗). Similarly, the canonical representation of the `∞ sum of `∞/c0 is the Banach space of continuous functions on the closure of any non-compact cozero subset of N∗. It is important to determine if there is a continuous linear lifting of this Banach space to a complemented subset of...