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FROM THE advent: "This quantity grew from a dialogue through the editors at the hassle of discovering solid thesis difficulties for graduate scholars in topology. even supposing at any given time we each one had our personal favourite difficulties, we said the necessity to supply scholars a much broader choice from which to settle on a subject matter ordinary to their pursuits. one in all us remarked, `Wouldn't or not it's great to have a publication of present unsolved difficulties regularly to be had to drag down from the shelf?' the opposite responded `Why do not we easily produce one of these book?' years later and never so easily, this is the ensuing quantity. The cause is to supply not just a resource publication for thesis-level difficulties but in addition a problem to the easiest researchers within the field."

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21 23 24 25 26 28 28 30 31 32 difficulties I want i'll clear up by way of S. Watson . . . . . . . . . . . . . . . . . . . 1. advent . . . . . . . . . . . . . . . . . . 2. basic now not Collectionwise Hausdorff areas three. Non-metrizable common Moore areas . . . . four. in the neighborhood Compact basic areas . . . . . . . five. Countably Paracompact areas . . . . . . . 6. Collectionwise Hausdorff areas . . . . . . . 7. Para-Lindel¨ of areas . . . . . . . . . . . . . eight. Dowker areas . . . . . . . . . . . . . . . . . nine. Extending beliefs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 39 forty forty three forty four forty seven 50 fifty two fifty four fifty five vii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii 10. Homeomorphisms eleven. Absoluteness . . . 12. Complementation thirteen. different difficulties . References . . . . . . . Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . fifty eight sixty one sixty three sixty eight sixty nine Weiss’ Questions via W. Weiss . . . . . . . . . . . . . . A. difficulties approximately uncomplicated areas . . . . B. difficulties approximately Cardinal Invariants C. difficulties approximately walls . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . seventy seven seventy nine eighty eighty one eighty three completely common compacta, cosmic areas, and a few partition by means of G. Gruenhage . . . . . . . . . . . . . . . . . . . . . . . 1. a few unusual Questions . . . . . . . . . . . . . . . . . . 2. completely basic Compacta . . . . . . . . . . . . . . . three. Cosmic areas and Coloring Axioms . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . difficulties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . eighty five 87 89 ninety one ninety four Open difficulties on βω by means of ok. P. Hart and J. van Mill . . . . . . . 1. creation . . . . . . . . . . . . . . . . 2. Definitions and Notation . . . . . . . . . three. solutions to older difficulties . . . . . . . . four. Autohomeomorphisms . . . . . . . . . . . five. Subspaces . . . . . . . . . . . . . . . . . . 6. person Ultrafilters . . . . . . . . . . . 7. Dynamics, Algebra and quantity idea . eight. different . . . . . . . . . . . . . . . . . . . . nine. Uncountable Cardinals . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ninety seven ninety nine ninety nine a hundred 103 one zero five 107 109 111 118 one hundred twenty On first countable, countably compact areas III: the matter of acquiring separable noncompact examples through P. Nyikos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Topological historical past . . . . . . . . . . . . . . . . . . . . . . . . 2. The γN development. . . . . . . . . . . . . . . . . . . . . . . . . . three. The Ostaszewski-van Douwen development. . . . . . . . . . . . . . four. The “dominating reals” buildings. . . . . . . . . . . . . . . . . five. Linearly ordered remainders . . . . . . . . . . . . . . . . . . . . . 6. Difficulties with manifolds . . . . . . . . . . . . . . . . . . . . . . 7. within the No Man’s Land . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 131 132 134 a hundred and forty 146 152 157 159 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Contents ix Set-theoretic difficulties in Moore areas by means of G. M. Reed . . . . . . . . . . . . . . . . . . . . . . 1. creation . . . . . . . . . . . . . . . . . . . . . . 2. Normality . . . . . . . . . . . . . . . . . . . . . . . . three. Chain stipulations . . . . . . . . . . . . . . . . . . . four. The collectionwise Hausdorff estate . . . . . . . . five. Embeddings and subspaces . . . . . . . . . . . . . . 6. The point-countable base challenge for Moore areas 7.

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