By Jan van Mill, George M. Reed

ISBN-10: 0444887687

ISBN-13: 9780444887689

This quantity grew from a dialogue through the editors at the trouble of discovering solid thesis difficulties for graduate scholars in topology. even though at any given time we each one had our personal favourite difficulties, we stated the necessity to provide scholars a much broader choice from which to decide on a subject bizarre to their pursuits. one among us remarked, `Wouldn't or not it's great to have a booklet of present unsolved difficulties continually on hand to drag down from the shelf?' the opposite answered `Why don't we easily produce the sort of book?' years later and never so easily, this is the ensuing quantity. The cause is to supply not just a resource booklet for thesis-level difficulties but additionally a problem to the easiest researchers within the box.

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**Example text**

Dowker Spaces . . . . . . . . . 9. Extending Ideals . . . . . . . . 10. Homeomorphisms . . . . . . . . 11. Absoluteness . . . . . . . . . 12. Complementation . . . . . . . . 13. Other Problems . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

46, 294–298. [1982] If all normal Moore spaces are metrizable, then there is an inner model with a measurable cardinal. Trans. Amer. Math. , 273, 365–373. [1983] Discrete sets of singular cardinality. Proc. Amer. Math. , 88, 743–745. [1984] The Normal Moore space conjecture and large cardinals. In Handbook of Set-Theoretic Topology, K. Kunen and J. E. Vaughan, editors, chapter 16, pages 733–760. North-Holland, Amsterdam. Fleissner, W. G. and S. Shelah. [19∞] Collectionwise Hausdorﬀ: incompactness at singulars.

I think the answer is yes. This belief stems from Watson [1982] where an intimate relation between the two existence problems was shown. The only thing that is missing is the possibility that there might be a model in which normal ﬁrst countable spaces are ℵ1 -collectionwise Hausdorﬀ and yet that in that model there is a normal ﬁrst countable space which fails to be ℵ2 -collectionwise Hausdorﬀ. This seems unlikely, though it is open, and yet the question might be answered positively in any case (see Shelah [1977]).

### Open Problems in Topology by Jan van Mill, George M. Reed

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