The ``Way-Below'' Relation

Grzegorz Bancerek

Warsaw University, Bialystok

Summary.

In the paper the ``way-below" relation, in symbols $x \ll y$, is introduced. Some authors prefer the term ``relatively compact" or ``way inside", since in the poset of open sets of a topology it is natural to read $U \ll V$ as ``$U$ is relatively compact in $V$". A compact element of a poset (or an element isolated from below) is defined to be way below itself. So, the compactness in the poset of open sets of a topology is equivalent to the compactness in that topology.\par The article includes definitions, facts and examples 1.1-1.8 presented in [11, pp. 38-42].

This work has been partially supported by Office of Naval Research Grant N00014-95-1-1336.

MML Identifier: WAYBEL_3

Contents (PDF format)

1. The ``Way-Below'' Relation
2. The Way-Below Relation in Other Terms
3. Continuous Lattices
4. The Way-Below Relation in Direct Powers
5. The Way-Below Relation in Topological Spaces

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