Separating maps and the nonarchimedean Hewitt theorem
Some problems and lines of investigation in general topology
Some properties of the ideal of continuous functions with pseudocompact support.
Some properties of the remainder of Stone-Čech compactifications
Some remarks on almost radiality in function spaces
Some set-theoretic constructions in topology
Spaces in which all prime -ideals of are minimal or maximal
Quasi -spaces are defined to be those Tychonoff spaces such that each prime -ideal of is either minimal or maximal. This article is devoted to a systematic study of these spaces, which are an obvious generalization of -spaces. The compact quasi -spaces are characterized as the compact spaces which are scattered and of Cantor-Bendixson index no greater than 2. A thorough account of locally compact quasi -spaces is given. If is a cozero-complemented space and every nowhere dense zeroset...
Structure spaces for rings of continuous functions with applications to realcompactifications
Let X be a completely regular space and let A(X) be a ring of continuous real-valued functions on X which is closed under local bounded inversion. We show that the structure space of A(X) is homeomorphic to a quotient of the Stone-Čech compactification of X. We use this result to show that any realcompactification of X is homeomorphic to a subspace of the structure space of some ring of continuous functions A(X).
Super real closed rings
A super real closed ring is a commutative ring equipped with the operation of all continuous functions ℝⁿ → ℝ. Examples are rings of continuous functions and super real fields attached to z-prime ideals in the sense of Dales and Woodin. We prove that super real closed rings which are fields are an elementary class of real closed fields which carry all o-minimal expansions of the real field in a natural way. The main part of the paper develops the commutative algebra of super real closed rings, by...
Sur la transformation de Dirac d'un espace à génération compacte
SV and related -rings and spaces
An -ring is an SV -ring if for every minimal prime -ideal of , is a valuation domain. A topological space is an SV space if is an SV -ring. SV -rings and spaces were introduced in [HW1], [HW2]. Since then a number of articles on SV -rings and spaces and on related -rings and spaces have appeared. This article surveys what is known about these -rings and spaces and introduces a number of new results that help to clarify the relationship between SV -rings and spaces and related...