Essential permutation preserves a convergence just on a set of the first category in the space of series

The authors resultthat the set of unconditionally convergent series is of the first category in the space of convergent series with the supremum-norm isstrengthening. It is proved that the set of all series, which preserve convergence under a fixed permutation, has the same property, ifthat permutation changed a convergence. This result is true for a space of series in each Banach space.

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