Abstract
Whenever, of any two zero-sets of a space X whose union is all of X at least one is open, then we call the space X a PF-space. We show that PF-spaces are precisely F-spaces in which all but at most one point is a P-point. As algebraic characterizations of PF-spaces, it is shown in this paper that X is a PF-space if and only if, of any two ideals in C(X) whose sum (intersection) is a proper z-ideal at least one of them is a z-ideal or equivalently, of any two ideals in C(X) whose product is a P-ideal, at least one is a P-ideal. These are also equivalent to saying that of any two comaximal principal ideals of C(X), one is semiprime and the other is convex. The relations between PF-spaces and other familiar spaces are investigated and we observe that a space is a cozero complemented PF-space if and only if it is a basically disconnected essential almost P-space (a space in which at most one point fails to be an almost P-point).
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callSimilar Papers
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
