spaces and the vanishing of the functor Ext
There are defined sequential moduli in the remainder form for real sequences. Properties of sequence spaces generated by means of the above moduli are investigated.
We investigate the extent to which sequence spaces are determined by the sequences of 0's and 1's that they contain.
In [3] it was discovered that one of the main results in [1] (Theorem 5.2), applied to three spaces, contains a nontrivial gap in the argument, but neither the gap was closed nor a counterexample was provided. In [4] the authors verified that all three above mentioned applications of the theorem are true and stated a problem concerning the topological structure of one of these three spaces. In this paper we answer the problem and give a counterexample to the theorem in doubt. Also we establish a...