Is the theory of topological vector spaces still alive?



Dear colleagues,

A few years ago I wrote a paper where the theory of topological vector
spaces was called a dead science:

S.S.Akbarov. Pontryagin duality in the theory of topological vector
spaces and in topological algebra. Journal of Mathematical Sciences.
113(2): 179--349 (2003).

After its publication I received two protests from two mathematicians
who specialized in this science. That was a big surprise for me, since
for a long time my criticism at this address did not meet any
protests.

Unfortunately in both cases the discussion stopped at the stage of
specification of claims. However this question -- whether the theory
of topological vector spaces is dead or alive? -- intrigues me very
much. Perhaps, the picture from Russia looks somewhat more sorrowful
than it really is, so I am curious now if there are any people abroad
who could argue with me?

My point is that the main results in this theory were formulated in
1960s, and now people either apply them to other disciplines, or,
those few who remain faithful, study things useless for remaining
mathematics.

I am writing now another paper where I plan to mention this question
casually, so I will be grateful to everybody who could discuss this
with me.

Thank you in advance,
Sergei Akbarov

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