Open Problems in Topology

FROM THE creation: "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 though at any given time we every one had our personal favourite difficulties, we stated the necessity to provide scholars a much wider choice from which to decide on a subject unusual to their pursuits. certainly one of us remarked, `Wouldn't or not it's great to have a booklet of present unsolved difficulties regularly to be had to drag down from the shelf?' the opposite spoke back `Why do not we easily produce the sort of book?' years later and never so easily, this is the ensuing quantity. The motive is to supply not just a resource publication for thesis-level difficulties but additionally a problem to the simplest researchers within the field."

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Bell, M. G. [1982] the gap of whole subgraphs of a graph. Comm. Math. Univ. Carolinae, 23, 525–536. [19∞] A first countable compact area that's not an Æ∗ photograph. best. Appl. to seem. Bell, M. G. and ok. Kunen. [1981] at the pi-character of ultrafilters. C. R. Math. Rep. Acad. Sci. Canada, three, 351–356. Bellamy, D. [1971] An non-metric indecomposable continuum. Duke Math J. , 38, 15–20. References 121 Blass, A. [1986] close to Coherence of Filters I: cofinal equivalence of types of mathematics. Notre Dame J. Formal common sense, 27, 579–591.

431 434 437 440 447 450 a listing of Open difficulties fit thought via J. Dydak and J. Segal . . . . . . . . . . 1. Cohomological and form dimensions . . 2. Movability and polyhedral form . . . . . three. form and powerful form equivalences . . four. P -like continua and form classifications . References . . . . . . . . . . . . . . . . . . . . Algebraic Topology by means of G. E. Carlsson . . . . . . . . 1. creation . . . . . . . . . . 2. challenge consultation for Homotopy three. H-spaces . . . . . . . . . . . . four. okay and L-theory . . . . . . . . five. Manifolds & Bordism . . . . . 6. Transformation teams . . . . 7. ok.

645 647 648 650 651 652 652 Index of basic phrases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 655 Index of phrases utilized in the issues . . . . . . . . . . . . . . . . . . . . . 673 Part I Set Theoretic Topology Contents: Dow’s Questions via A. Dow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . five Stepr¯ ans’ difficulties by way of J. Steprans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . thirteen Tall’s difficulties by means of F. D. Tall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 difficulties I want i'll clear up by way of S. Watson . . . . . . . . . . . . . . .

Additionally, considering the fact that |X| ≤ c (by separability and first countability) X has a base of countable, compact open units, we will take τ = |X| ≤ c. for example, first take an arbitrary well-ordered { yα : α < τ } the place { yn : n ∈ ω } is the set of all remoted issues. allow xn = yn for all n ∈ ω, and if Xα has been defined, permit ξ be the least ordinal such that yξ ∈ Xα . enable okay be a countable clopen local of yξ , and well-order ok \ Xα in order that preliminary segments are open, okay \ Xα = { xα+η : η < δ } for a few countable ordinal δ.

645 647 648 650 651 652 652 Index of normal phrases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 655 Index of phrases utilized in the issues . . . . . . . . . . . . . . . . . . . . . 673 Part I Set Theoretic Topology Contents: Dow’s Questions via A. Dow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . five Stepr¯ ans’ difficulties by way of J. Steprans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . thirteen Tall’s difficulties via F. D. Tall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 difficulties I want i may remedy through S. Watson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Weiss’ Questions via W.

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