By Jan van Mill, George M. Reed
This quantity grew from a dialogue by way of the editors at the hassle of discovering reliable thesis difficulties for graduate scholars in topology. even supposing at any given time we each one had our personal favourite difficulties, we stated the necessity to supply scholars a much wider choice from which to settle on a subject unusual to their pursuits. one among us remarked, `Wouldn't or not it's great to have a e-book of present unsolved difficulties constantly to be had to tug down from the shelf?' the opposite responded `Why don't we easily produce this type of book?' years later and never so easily, this is the ensuing quantity. The reason is to supply not just a resource ebook for thesis-level difficulties but additionally a problem to the easiest researchers within the box.
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This quantity grew from a dialogue via the editors at the hassle of discovering solid thesis difficulties for graduate scholars in topology. even supposing at any given time we every one had our personal favourite difficulties, we stated the necessity to provide scholars a much broader choice from which to settle on a subject unusual to their pursuits.
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Additional info for Open Problems in Topology
108. Another question which has not really been looked at but which I think is extremely important is: Problem 41. (Palermo #42) Are para-Lindel¨of collectionwise normal spaces 109. paracompact? This was ﬁrst asked by Fleissner and Reed . So far, there are no ideas at all on how to to approach this. Even the much weaker property of meta-Lindel¨of creates big problems here: Problem 42. (Palermo #58) Is it consistent that meta-Lindel¨of collection- 110. wise normal spaces are paracompact?
There is an example of a screenable space which is not normal in Bing  but a lot of work has to be done to make it para-Lindel¨ of. Maybe that is the place to start. Keep in mind that para-Lindel¨ of spaces are strongly collectiowise Hausdorﬀ (Fleissner and Reed ). 8. Dowker Spaces The next few questions are ZFC questions about Dowker spaces. It’s fairly easy to come up with a question about Dowker spaces.
These diﬃculties each gave rise to questions which were listed in Navy’s thesis. The main open problem listed above is due to the fact that all the constructions are intrinsically countably paracompact. I tried for a long time to build in the failure of countable paracompactness but each time para-Lindel¨ of failed as well. It may be useful to note that the whole idea of Navy’s construction was to take Fleissner’s space of Fleissner  which was σ-para-Lindel¨of but not paracompact and build in a way to “separate” the countably-many locally countable families so that one locally countable reﬁnement is obtained.
Open Problems in Topology by Jan van Mill, George M. Reed