Analytic geometry and principles of algebra by Alexander Ziwet, Louis Allen Hopkins

By Alexander Ziwet, Louis Allen Hopkins

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Using the expansion homotopies A → Nt (A), we see that X is a Z-set in 2X . If we now take the direct limit, we obtain a space which is homeomorphic to separable Hilbert space equipped with the bounded-weak topology and has an induced G action on it. Identify this action directly in terms of 2 . I5. (J. West [380]) If, in the situation of Problem I4, we take the metric direct limit, we have a separable metric space with a G action on it. Characterize this space and/or its completion in terms of more familiar objects.

Once the above is done, characterize the induced G action. I6. (H. Hastings [176]) Is every (weak) shape equivalence of compact metric spaces a strong shape equivalence? 32 contributed problems I7. (M. Jani [199]) Is there a cell-like shape fibration p : E → B from a compactum E onto the dyadic solenoid B, which is not a shape equivalence? I8. T. Rogers [316]) Is any nondegenerate, homogeneous contractible continuum homeomorphic to the Hilbert cube? I9. (H. Gladdines [147]) Let L(R2 ) denote the collection of Peano continua in R2 .

A reduced abelian group. If G admits a pseudocompact group topology, must G admit also a zero-dimensional pseudocompact group topology? L38. (D. Dikranjan and D. Shakhmatov [94]) Let G be a non-torsion pseudocompact abelian group. Do there exist a cardinal σ and a subset of cardinality r(G) of {0, 1}σ whose projection on every countable subproduct is a surjection? L39. (D. Dikranjan and D. Shakhmatov [94]) Characterize (abelian) groups which admit a group topology which has one of the following properties: countably compact, σ-compact, or Lindel¨ of.

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Analytic geometry and principles of algebra by Alexander Ziwet, Louis Allen Hopkins
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