Given a complex Banach space X, we investigate the stable character of property (VE) for bounded linear operator T:X→X, under commuting perturbations that are Riesz, compact, algebraic and hereditarily polaroid. We also analyze sufficient conditions allow transfer from tensorial factors T S to its tensor product.

The paper is organized as a self-contained literate Prolog program that implements elements of an executable finite set theory with focus on combinatorial generation and arithmetic encodings. The complete SWI-Prolog tested code is available at http://logic.csci.unt.edu/tarau/research/2008/pHFS.zip. First, ranking and unranking functions for some “mathematically elegant” data types in the univer...

Given a map T : X → X on a set X we examine under what conditions there is a separable metrizable or an hereditarily Lindelöf or a Lindelöf topology on X with respect to which T is a continuous map. For separable metrizable and hereditarily Lindelöf, it turns out that there is a such a topology precisely when the cardinality ofX is no greater than the cardinality of the continuum. We go onto pr...

A cardinal λ is called ω-inaccessible if for all µ < λ we have µ ω < λ. We show that for every ω-inaccessible cardinal λ there is a CCC (hence cardinality and cofinality preserving) forcing that adds a hereditarily Lindelöf regular space of density λ. This extends an analogous earlier result of ours that only worked for regular λ. In [1] we have shown that for any cardinal λ a natural CCC forci...

We prove a Bruckner-Garg type theorem for the fiber structure of a generic map from a continuum X into the unit interval I. We also study the specific case of X = S2. We show that each nondegenerate component of each fiber of a generic map in C(S2, I) is figure-eight-like. This together with a result by Krasinkiewicz and Levin gives that each nondegenerate component of each fiber of a generic m...

We consider the problem, raised by Kunen and Tall, of whether the real continuum can have non-homeomorphic versions in different submodels of the universe of all sets. This requires large cardinals, and we obtain an exact consistency strength: Theorem 1. The following are equiconsistent : (i) ZFC + ∃κ a Jónsson cardinal ; (ii) ZFC + ∃M a sufficiently elementary submodel of the universe of sets ...

In this paper we define a space σ(X) for approximate systems of compact spaces. The construction is due to H. Freudenthal for usual inverse sequences [4, p. 153–156]. We stablish the following properties of this space: (1) The space σ(X) is a paracompact space, (2) Moreover, if X is an approximate sequence of compact (metric) spaces, then σ(X) is a compact (metric) space (Lemma 2.4). We give th...