Tidten, Michael An example of a continuum of pairwise non-isomorphic spaces of \(C^{\infty}\)-functions. (English) Zbl 0599.46028 Stud. Math. 78, 267-274 (1984). There is given a family \((K_{\tau})\) of compact sets \(K_{\tau}\) in the Euclidean plane with \(\tau\) ranging in a real interval such that the Whitney spaces \({\mathcal E}(K_{\tau})\) are pairwise non-isomorphic. A successful distinction of the topological structures which is sufficient for this result is managed by a certain topological property involving an increasing monotone function on \(R_+\). After Zaharyuta had presented a continuum of pairwise non-isomorphic spaces of analytic functions the open question for an analogous example in the frame of \(C^{\infty}\)- functions is clarified by a positive answer. Cited in 2 Documents MSC: 46E10 Topological linear spaces of continuous, differentiable or analytic functions 46A04 Locally convex Fréchet spaces and (DF)-spaces Keywords:continuum of pairwise non-isomorphic spaces of \(C^{\infty }\)-functions; Whitney spaces PDFBibTeX XMLCite \textit{M. Tidten}, Stud. Math. 78, 267--274 (1984; Zbl 0599.46028) Full Text: DOI EuDML