TY - JOUR
AU - Raphael, R.
AU - Woods, R.G.
PY - 2006/04/01
Y2 - 2024/08/06
TI - On RG-spaces and the regularity degree
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 7
IS - 1
SE -
DO - 10.4995/agt.2006.1934
UR - https://polipapers.upv.es/index.php/AGT/article/view/1934
SP - 73-101
AB - <p>We continue the study of a lattice-ordered ring G(X), associated with the ring C(X). Following, X is called RG when G(X) = C(X<sub>δ</sub>). An RG-space must have a dense set of very weak P-points. It must have a dense set of almost-P-points if X<sub>δ</sub> is Lindelöf, or if the continuum hypothesis holds and C(X) has small cardinality. Spaces which are RG must have finite Krull dimension when taken with respect to the prime z-ideals of C(X). There is a notion of regularity degree defined via the functions in G(X). Pseudocompact spaces and metric spaces of finite regularity degree are characterized.</p>
ER -