Relative Properties
by
Paul Gartside
University of Pittsburgh
Coauthors: Aneirin Glyn (Oxford, UK)

We answer a number of questions posed by A.V. Arhangel'skii concerning relative topological properties. Typical of our results is a negative answer to:

Question: Let Y be a subspace of a Hausdorff space X such that every closed subset of X contained in Y is compact (in short, `Y is compact in X from inside'). Is then Y regular?

In the spirit of the Galway Colloquium, we will try to answer the `Why?' and `What next?' questions:

`Why consider relative properties?'

`What should we look at next?'

as well as the obvious `What are relative properties anyway?' and `How do you answer Arhangel'skii's questions?'.

Paper reference: atlas:ideb-92

Date received: August 23, 2000