For A ⊂ I = [0,1], let be the set of continuous real-valued functions on I which vanish on a neighborhood of A. We prove that if A is an analytic subset which is not an and whose closure has an empty interior, then is homeomorphic to the space of differentiable functions from I into ℝ.
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...