Some Screenable, Σ-relatively Discrete Dowker Spaces

A Screenable, Σ-relatively Discrete Dowker Space

A Dowker space (that is, a normal space that is not countably metacompact) is constructed which is also screenable and the countable union of discrete subspaces. The construction and proofs are easy modifications of the ones for Balogh’s screenable Dowker space [B1]. Balogh’s example is presented alongside the modification in a new exposition with several new results common to the two spaces, i...

σ-Normality of Topological Spaces

Large Cardinals and Small Dowker Spaces

We prove that, if there is a model of set-theory which contains no first countable, locally compact, scattered Dowker spaces, then there is an inner model which contains a measurable cardinal. A Hausdorff space is normal if, for every pair of disjoint closed sets C and D, there is a pair of disjoint open sets, U containing C and V containing D. A (normal) space is binormal if its product with t...

Geometric and Higher Order Logic in terms of Abstract Stone Duality

The contravariant powerset, and its generalisations Σ to the lattices of open subsets of a locally compact topological space and of recursively enumerable subsets of numbers, satisfy the Euclidean principle that φ ∧ F (φ) = φ ∧ F (>). Conversely, when the adjunction Σ(−) a Σ(−) is monadic, this equation implies that Σ classifies some class of monos, and the Frobenius law ∃x.(φ(x) ∧ ψ) = (∃x.φ(x...

Classical polar spaces (sub–)weakly embedded in projective spaces

In this paper we are concerned with classical polar spaces, i. e. with the set of points and lines of some vector space W on which a non–degenerate (σ, )-hermitian form or pseudo-quadratic form vanishes. To state the Main Theorem we introduce some notation. Let L be a division ring and W be a (left–)vector space over L endowed with a (σ, )–hermitian form or a pseudo–quadratic form q (with assoc...