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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| Format: | Article |
| Language: | English |
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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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| _version_ | 1832564854474407936 |
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| author | Philippe Gaucher |
| author_facet | Philippe Gaucher |
| author_sort | Philippe Gaucher |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-d22ff61cb72541ef82972bd1c013a1ae |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-d22ff61cb72541ef82972bd1c013a1ae2025-02-03T01:10:07ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252007-01-01200710.1155/2007/8740487404T-Homotopy and Refinement of Observation—Part II: Adding New T-Homotopy EquivalencesPhilippe Gaucher0Preuves Programmes et Systèmes, Université Paris 7–Denis Diderot, Case 7014, 2 Place Jussieu, Paris Cedex 05 75251, FranceThis 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.http://dx.doi.org/10.1155/2007/87404 |
| spellingShingle | Philippe Gaucher T-Homotopy and Refinement of Observation—Part II: Adding New T-Homotopy Equivalences International Journal of Mathematics and Mathematical Sciences |
| title | T-Homotopy and Refinement of Observation—Part II: Adding New T-Homotopy Equivalences |
| title_full | T-Homotopy and Refinement of Observation—Part II: Adding New T-Homotopy Equivalences |
| title_fullStr | T-Homotopy and Refinement of Observation—Part II: Adding New T-Homotopy Equivalences |
| title_full_unstemmed | T-Homotopy and Refinement of Observation—Part II: Adding New T-Homotopy Equivalences |
| title_short | T-Homotopy and Refinement of Observation—Part II: Adding New T-Homotopy Equivalences |
| title_sort | t homotopy and refinement of observation part ii adding new t homotopy equivalences |
| url | http://dx.doi.org/10.1155/2007/87404 |
| work_keys_str_mv | AT philippegaucher thomotopyandrefinementofobservationpartiiaddingnewthomotopyequivalences |