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On noncontractible compacta with trivial homology and homotopy groups

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 نشر من قبل Du\\v{s}an Repov\\v{s}
 تاريخ النشر 2009
  مجال البحث
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We construct an example of a Peano continuum $X$ such that: (i) $X$ is a one-point compactification of a polyhedron; (ii) $X$ is weakly homotopy equivalent to a point (i.e. $pi_n(X)$ is trivial for all $n geq 0$); (iii) $X$ is noncontractible; and (iv) $X$ is homologically and cohomologically locally connected (i.e. $X$ is a $HLC$ and $clc$ space). We also prove that all classical homology groups (singular, v{C}ech, and Borel-Moore), all classical cohomology groups (singular and v{C}ech), and all finite-dimensional Hawaiian groups of $X$ are trivial.



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