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A few problems concerning linear topological spaces. (Japanese) Zbl 0135.34302
Sûgaku 15, 218-221 (1964).
In this paper the author gives an expository account of certain problems in G. Köthe’s book on linear topological spaces [Topologische lineare Räume. I. Springer, Berlin (1960; Zbl 0093.11901)], and reports that most of these problems are answered negatively by constructing counterexamples. An example of a barrelled (DF)-space which is not bornological and an example of a non-complete Montel space are shown explicitly. It is also mentioned that an example of a bornological space whose completion is not bornological can be constructed under the assumption of the continuum hypothesis. This paper is essentially a summary of contents of papers by the author [Kumamoto J. Sci., Math. 5, 148–157 (1962; Zbl 0105.30803); Math. Ann. 153, 150–162 (1964; Zbl 0149.33604)] and also a paper by T. Kōmura and the author [J. Math. Soc. Japan 15, 319–338 (1963; Zbl 0117.07702)].
MSC:
46Axx Topological linear spaces and related structures