Abstract
This paper is concerned with some questions of regularity in increasing inductive sequences of locally convex spaces. It is shown that the various stronger terms of regularity coincide in case of normed steps and are equivalent with property (M) defined by Retakh which turned out to be basical in the topology problem of a subspace and well-location. Some of these results keep validity even in more general cases. Finally, an example of a regular but not sequentially-retractive (LB)-space is given answering some open related questions as well.
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Neus, H. Über die Regularitatsbegriffe induktiver lokalkonvexer Sequenzen. Manuscripta Math 25, 135–145 (1978). https://doi.org/10.1007/BF01168605
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DOI: https://doi.org/10.1007/BF01168605