TY - JOUR
AU - Abohalfya, F.
AU - Raphael, R.
PY - 2012/04/15
Y2 - 2022/11/30
TI - Aspects of RG-spaces
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 13
IS - 1
SE -
DO - 10.4995/agt.2012.1637
UR - http://ojs.upv.es/index.php/AGT/article/view/1637
SP - 39-49
AB - <p>A Tychonoff space X which satisfies the property that G(X) = C(Xδ) is called an RG-space, where G(X) is the minimal regular ring extension of C(X) inside F(X), the ring of all functions from X to R, and Xδ is the topology on X generated by its Gδ-sets. We correct an error tha twe found in the proof of and show that RG-spaces must satisfy a finite dimensional condition.</p><p>We also introduce a new class of topological spaces which we call almost k-Baire spaces. The class of almost Baire spaces is a particular instance. We show that every RG-space is an almost Baire space but not necessarily a Baire space. However RG-spaces of countable pseudocharacter must be Baire and, furthermore, their dense sets have dense interiors.</p>
ER -