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From reading the literature of the 1970s heyday of locally convex spaces, it seems that it was an important open question whether there is an infra-Pták (i.e. $B_r$-complete) space that is not Pták (i.e. $B$-complete). Is this still open?

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    $\begingroup$ Could you please recall the definitions? I would first check to book Barrelled Locally Convex Spaces of Bonet and Perez-Carreras. $\endgroup$
    – Jochen Wengenroth
    Commented Apr 19, 2020 at 21:21
  • $\begingroup$ @JochenWengenroth Thanks for the book reference. I hadn't seen it before, but it looks like it contains a lot of the harder-to-find later results of the Iberian school of TVS theory. $\endgroup$
    – Cameron Zwarich
    Commented Apr 25, 2020 at 15:20

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Valdivia constructed counterexamples in his paper Br-Complete Spaces which are not B-Complete.

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