Abstract
We use N -compactifications of 0-dimensional spaces to obtain a new shape invariant for the class of all topological spaces. We also point out that the shape and topological classifications are not the same in the realm of Tychonov spaces having a base of clopen sets. Finally we use the new shape invariant to obtain classes of spaces where the conditions “to have the same shape” and “to be homeomorphic” are equivalent.
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