T-Homotopy and Refinement of Observation—Part II: Adding New T-Homotopy Equivalences
This paper is the second part of a series of papers about a new notion of T-homotopy of flows. It is proved that the old definition of T-homotopy equivalence does not allow the identification of the directed segment with the 3-dimensional cube. This contradicts a paradigm of dihomotopy theory. A new...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2007-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2007/87404 |
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| Summary: | This paper is the second part of a series of papers about a new
notion of T-homotopy of flows. It is proved that the old definition
of T-homotopy equivalence does not allow the identification of the
directed segment with the 3-dimensional cube. This contradicts a
paradigm of dihomotopy theory. A new definition of T-homotopy
equivalence is proposed, following the intuition of refinement of
observation. And it is proved that up to weak S-homotopy, an old
T-homotopy equivalence is a new T-homotopy equivalence. The
left properness of the weak S-homotopy model category of flows is
also established in this part. The latter fact is used
several times in the next papers of this series. |
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| ISSN: | 0161-1712 1687-0425 |