Some set-theoretic constructions in topology

On The Modal Logics of Some Set-Theoretic Constructions

Some Problems and Techniques in Set-theoretic Topology

I survey some problems and techniques that have interested me over the years, e.g. normality vs. collectionwise normality, reflection, preservation by forcing, forcing with Souslin trees, and Lindelöf problems.

Order-theoretic Invariants in Set-theoretic Topology

We present several results related to van Douwen’s Problem, which asks whether there is homogeneous compactum with cellularity exceeding c, the cardinality of the reals. For example, just as all known homogeneous compacta have cellularity at most c, they satisfy similar upper bounds in terms of Peregudov’s Noetherian type and related cardinal functions defined by order-theoretic base properties...

Part I Set Theoretic Topology

Lecture 5: Some Basic Constructions in Symplectic Topology

In complex geometry the blowing-up operation amounts to replace a point in a space by the space of complex tangent lines through that point. It is a local operation which can be explicitly written down as follows. Consider the blow-up of Cn at the origin. This is the complex submanifold of Cn × CPn−1 C̃ ≡ {((z1, z2, · · · , zn), [w1, w2, · · · , wn])|(z1, z2, · · · , zn) ∈ [w1, w2, · · · , wn]}....