Kucera, Jan Ultraregular inductive limits. (English) Zbl 0713.46007 Int. J. Math. Math. Sci. 13, No. 1, 51-54 (1990). Let \(E_ 1\subset E_ 2\subset..\). be a sequence of locally convex spaces with continuous inclusions and E the corresponding inductive limit. E is said to be ultraregular if each bounded subset of E is contained and bounded in some \(E_ n\). It is proved that if each \(E_ n\) is closed in \(E_{n+1}\) and each \(E_ n\) is an LF-space, then E is ultraregular if and only if every absolutely convex closed neighborhood of \(E_ n\) is closed in \(E_{n+1}\). Reviewer: T.Terzioglu MSC: 46A13 Spaces defined by inductive or projective limits (LB, LF, etc.) 46A04 Locally convex Fréchet spaces and (DF)-spaces Keywords:inductive limit; ultraregular; bounded subset PDFBibTeX XMLCite \textit{J. Kucera}, Int. J. Math. Math. Sci. 13, No. 1, 51--54 (1990; Zbl 0713.46007) Full Text: DOI EuDML