A locally connected continuum without convergent sequences

We answer a question of Juhasz by constructing under CH an example of a locally connected continuum without nontrivial convergent sequences.Comment: 6 pages. Reprinted from Topology and its Applications, in press, Jan van Mill, A locally connected continuum without convergent sequence

A homogeneous space whose complement is rigid

We construct a homogeneous subspace of $2^\omega$ whose complement is dense in $2^\omega$ and rigid. Using the same method, assuming Martin's Axiom, we also construct a countable dense homogeneous subspace of $2^\omega$ whose complement is dense in $2^\omega$ and rigid.Comment: 9 page

Forbidden rectangles in compacta

We establish negative results about "rectangular" local bases in compacta. For example, there is no compactum where all points have local bases of cofinal type \omega x \omega_2. For another, the compactum \beta\omega has no nontrivially rectangular local bases, and the same is consistently true of \beta\omega \ \omega: no local base in \beta\omega has cofinal type \kappa x c if \kappa < m_{\sigma-n-linked} for some n in [1,\omega). Also, CH implies that every local base in \beta\omega \ \omega has the same cofinal type as one in \beta\omega. We also answer a question of Dobrinen and Todorcevic about cofinal types of ultrafilters: the Fubini square of a filter on \omega always has the same cofinal type as its Fubini cube. Moreover, the Fubini product of nonprincipal P-filters on \omega is commutative modulo cofinal equivalence.Comment: 15 page

Sleep, depression and anxiety: an epidemiological perspective

Penninx, B.W.J.H. [Promotor]Hoogendijk, W.J.G. [Promotor]Vogelzangs, N. [Copromotor