Metacompact subspaces of products of ordinals

Normal subspaces in products of two ordinals

Let λ be an ordinal number. It is shown that normality, collectionwise normality and shrinking are equivalent for all subspaces of (λ+ 1)2.

Countable Box Products of Ordinals 123

The countable box product of ordinals is examined in the paper for normality and paracompactness. The continuum hypothesis is used to prove that the box product of countably many a-compact ordinals is paracompact and that the box product of another class of ordinals is normal. A third class trivially has a nonnormal product Because I have found a countable box product of ordinals useful in the ...

Incompressibility of Products by Grassmannians of Isotropic Subspaces

We prove that the product of an arbitrary projective homogeneous variety Y by an orthogonal, symplectic, or unitary Grassmannian X is 2-incompressible if and only if the varieties XF (Y ) and YF (X) are so. Some new properties of incompressible Grassmannians are established on the way.

Comment on frame's of subspaces

Refined Intersection Products and Limiting Linear Subspaces of Hypersurfaces

LetX be a hypersurface of degree d in P and FX be the scheme of P ’s contained in X . If X is generic, then FX will have the expected dimension (or empty) and its class is given by the top Chern class of the vector bundle SymU∗, where U is the universal subbundle on the Grassmannian G(r + 1, n+ 1). Things become more interesting when X degenerates. For example, when we deform a generic X into a...