Orderability of all noncompact images

AbstractWe characterize the noncompact spaces whose every noncompact image is orderable as the noncompact continuous images of ω1. We find other useful characterizations as well. We also characterize the continuous images of ω1 + 1

P-remote points of X

AbstractA new inductive technique is given for the construction of certain kinds of special points in the Čech-Stone compactification of X. This technique significantly simplifies the proofs of some known results on remote points and is also used to show that noncompact first-countable spaces without isolated points have far points

P-remote points of X

AbstractA new inductive technique is given for the construction of certain kinds of special points in the Čech-Stone compactification of X. This technique significantly simplifies the proofs of some known results on remote points and is also used to show that noncompact first-countable spaces without isolated points have far points

Better closed ultrafilters on Q

AbstractCMA (Martin's Axiom for countable posets) implies that for each nϵN there is a free maximal closed filter on the space Q such that the filter it generates on the set Q is the intersection of n ultrafilters

A decomposition theorem for compact groups with application to supercompactness

We show that every compact connected group is the limit of a continuous inverse sequence, in the category of compact groups, where each successor bonding map is either an epimorphism with finite kernel or the projection from a product by a simple compact Lie group. As an application, we present a proof of an unpublished result of Charles Mills from 1978: every compact group is supercompact.Comment: 12 page

A convergence on Boolean algebras generalizing the convergence on the Aleksandrov cube

We compare the forcing related properties of a complete Boolean algebra B with the properties of the convergences $\lambda_s$ (the algebraic convergence) and $\lambda_{ls}$ on B generalizing the convergence on the Cantor and Aleksandrov cube respectively. In particular we show that $\lambda_{ls}$ is a topological convergence iff forcing by B does not produce new reals and that $\lambda_{ls}$ is weakly topological if B satisfies condition $(\hbar)$ (implied by the ${\mathfrak t}$-cc). On the other hand, if $\lambda_{ls}$ is a weakly topological convergence, then B is a $2^{\mathfrak h}$-cc algebra or in some generic extension the distributivity number of the ground model is greater than or equal to the tower number of the extension. So, the statement "The convergence $\lambda_{ls}$ on the collapsing algebra B=\ro ((\omega_2)^{<\omega}) is weakly topological" is independent of ZFC

The Collins-Roscoe mechanism and D-spaces

We prove that if a space X is well ordered $(\alpha A)$, or linearly semi-stratifiable, or elastic then X is a D-space

Some new directions in infinite-combinatorial topology

We give a light introduction to selection principles in topology, a young subfield of infinite-combinatorial topology. Emphasis is put on the modern approach to the problems it deals with. Recent results are described, and open problems are stated. Some results which do not appear elsewhere are also included, with proofs.Comment: Small update