On set tightness and $T$-tightness

The main purpose of this note is to study the behaviour of the set tightness and the T-tightness under maps and products.A particular result is the following: if X is a compact space and Y a Hausdorff space then t (XxY)t(X)t g (Y) and T(X^Y)^ T(X)(T(YJ.Finally a little bit refined version of two results in 3uhsz's first book concerning the depth of a topological space is given.

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