How to construct point finite covering in collectionwise normal spaces?

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How to construct point finite covering in collectionwise normal spaces

I am actually looking for a related reference (and ideally if anyone knows the answer) on the following construction problem: Let X= $\prod_{i=1,..,n} X_{i}$ be a collectionwise normal and Hausdorff locally convex topological vector space and for every $i \in$ {1,...,n} let $X_{i}$ be just a Hausdorff locally convex topological vector space. In addition let's assume for every $i \in$ {1,...,n} an upper semicontinuous multivalued map $\phi_{i}$:X-> $P(X_{i})$, with $\phi_{i}$(x) non-empty, convex...

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It seems the following. The families $\phi_i$ are not used in the question and the condition “$X_i$...

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Rnst at Mathematics Mark as irrelevant Undo

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