Timeline for What is a continuous path?
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| Nov 13, 2011 at 15:25 | history | edited | Eric Wofsey | CC BY-SA 3.0 |
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| Nov 13, 2011 at 15:17 | comment | added | Tim Porter | Strong homology is another name (or a slight variant of) Steenrod-Sitnikov homology. It can (approximately) be defined by taking the Vietoris (or Cech) inverse system of chain complexes and then taking their homology limit. Finally you take the homology of the result. This needs the fact that the Cech nerve forms a homotopy coherent diagram indexed by the directed set of open covers. | |
| Nov 13, 2011 at 13:06 | comment | added | Tim Porter | Agreeing with David Roberts, there is a large amount of literature on this (see also shape theory and strong shape theory) plus old work by Borsuk on intrinsic homotopy (if I remember rightly). Locally finite spaces may be useful, but play down on the metric. | |
| Nov 12, 2011 at 23:57 | comment | added | David Roberts♦ | Also: Čech homotopy ncatlab.org/nlab/show/%C4%8Cech+homotopy | |
| Nov 12, 2011 at 23:18 | comment | added | Valerio Capraro | Eric, many thanks for the detailed answer. I didn't know about such things. Tomorrow I will have a look at them in details. | |
| Nov 12, 2011 at 21:56 | history | edited | Eric Wofsey | CC BY-SA 3.0 |
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| Nov 12, 2011 at 21:44 | history | edited | Eric Wofsey | CC BY-SA 3.0 |
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| Nov 12, 2011 at 21:37 | history | answered | Eric Wofsey | CC BY-SA 3.0 |