Geometry from Africa (Classroom Resource Materials) by Paulus Gerdes

By Paulus Gerdes

This e-book attracts on geometric rules from cultural actions from Subsaharan Africa, and demonstrates how they're explored to increase mathematical reasoning from tuition point via to school common. Paulus Gerdes offers a completely illustrated and researched exploration of mathematical rules, motifs and styles. Many very important mathematical issues are dropped at the fore, now not through the formal 'theorem-proof' technique, yet in a extra schematic and diagrammatic demeanour. African artifacts, oral traditions, sand drawing and other kinds of art with a geometrical foundation, all offer mathematical principles for dialogue during this certain publication. Mathematicians and academics of arithmetic in any respect degrees can be involved, as will anyone with an curiosity in African cultures.

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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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Geometry from Africa (Classroom Resource Materials) by Paulus Gerdes
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