More topological cardinal inequalities

More on Cardinal Arithmetic Sh410

Two cardinal inequalities for functionally Hausdorff spaces

In this paper, two cardinal inequalities for functionally Hausdorff spaces are established. A bound on the cardinality of the τθ-closed hull of a subset of a functionally Hausdorff space is given. Moreover, the following theorem is proved: ifX is a functionally Hausdorff space, then |X| ≤ 2χ(X)wcd(X).

Scales, Topological Reflections, and Large Cardinal Issues

Reflection theorems in set-theoretic topology typically take the following form: if all “small” subspaces of a suitable kind of space X have a property P, then so does the whole space. Here “small” often means “of cardinality א1” but in Sections 1 and 2 of this paper it will mean “separable”. Usually, but not always, some sort of large cardinal axiom is needed, and the reflection theorem holds ...

More on Cardinal Invariants of Boolean Algebras

We address several questions of Donald Monk related to irredundance and spread of Boolean algebras, gaining both some ZFC knowledge and consistency results. We show in ZFC that irr(B0 × B1) = max{irr(B0), irr(B1)}. We prove consistency of the statement “there is a Boolean algebra B such that irr(B) < s(B ~ B)” and we force a superatomic Boolean algebra B∗ such that s(B∗) = inc(B∗) = κ, irr(B∗) ...

More inequalities for Laplacian indices by way of majorization

The n-tuple of Laplacian characteristic values of a graph is majorized by the conjugate sequence of its degrees. Using that result we find a collection of general inequalities for a number of Laplacian indices expressed in terms of the conjugate degrees, and then with a maximality argument, we find tight general bounds expressed in terms of the size of the vertex set n and the average degree dG...