  CWH, CWN stand for collectionwise Hausdorff and collectionwise normal
respectively. We analyze the statement "there is a lambda-CWH not CWH first
countable (Hausdorff topological) space". We prove the existence of such a
space under various conditions, show its equivalence to: there is a lambda-CWN
not CWN first countable space and give an equivalent set theoretic statement;
the nicest version we can obtain is in \S4. The author had a flawed proof of
the existence of such spaces in ZFC, for some lambda > aleph_1, in June of
1992; still we decided that there is some interest in the correct part and some
additions.
