The Vietoris system in strong shape and strong homology

• Autorzy: Bernd Günther
• Języki publikacji: EN

Abstrakty

EN

We show that the Vietoris system of a space is isomorphic to a strong expansion of that space in the Steenrod homotopy category, and from this we derive a simple description of strong homology. It is proved that in ZFC strong homology does not have compact supports, and that enforcing compact supports by taking limits leads to a homology functor that does not factor over the strong shape category. For compact Hausdorff spaces strong homology is proved to be isomorphic to Massey's homology.

Słowa kluczowe

EN

vietoris nerve; Steenrod homotopy category; strong shape theory; strong homology; compact supports

Kategorie tematyczne

• 55P55: Shape theory
• 55U35: Abstract and axiomatic homotopy theory
• 55N07: Steenrod-Sitnikov homologies
• 55U15: Chain complexes

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1992
• Tom: 141
• Numer: 2
• Strony: 147-168

Daty

wydano

1992

otrzymano

1991-08-12

Twórcy

autor

Bernd Günther

• Fachbereich Mathematik, Johann Wolfgang Goethe-Universität, Robert-Mayer-Strasse, 6-10 6000 Frankfurt, Germany

Bibliografia

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