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The functor $$\sigma^ 2 X$$. (English) Zbl 0839.46009
Summary: We disprove the existence of a universal object in several classes of spaces including the class of weakly Lindelöf-Banach spaces.

##### MSC:
 46B03 Isomorphic theory (including renorming) of Banach spaces 46M15 Categories, functors in functional analysis 46B25 Classical Banach spaces in the general theory 46B26 Nonseparable Banach spaces 46E15 Banach spaces of continuous, differentiable or analytic functions 54B99 Basic constructions in general topology 54C35 Function spaces in general topology 46A50 Compactness in topological linear spaces; angelic spaces, etc.
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