I have come across this thread about TVS. The OP took below screenshot of THEOREM 32.2.
Could you please elaborate on the book from which the screenshot was taken?
2026-03-26 09:58:06.1774519086
Textbook on TVS that contains Theorem 32.2 about the completeness of the space of continuous linear maps
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It's at page 343 and in section 32 Equicontinuous Sets of Linear Mappings of Francois Treves's Topological Vector Spaces, Distributions and Kernels.