Coherent and strong expansions of spaces coincide
Mardešić, Sibe
Fundamenta Mathematicae, Tome 158 (1998), p. 69-80 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

In the existing literature there are several constructions of the strong shape category of topological spaces. In the one due to Yu. T. Lisitsa and S. Mardešić [LM1-3] an essential role is played by coherent polyhedral (ANR) expansions of spaces. Such expansions always exist, because every space admits a polyhedral resolution, resolutions are strong expansions and strong expansions are always coherent. The purpose of this paper is to prove that conversely, every coherent polyhedral (ANR) expansion is a strong expansion. This result is obtained by showing that a mapping of a space into a system, which is coherently dominated by a strong expansion, is itself a strong expansion.

Publié le : 1998-01-01
EUDML-ID : urn:eudml:doc:212303 
@article{bwmeta1.element.bwnjournal-article-fmv158i1p69bwm,
     author = {Sibe Marde\v si\'c},
     title = {Coherent and strong expansions of spaces coincide},
     journal = {Fundamenta Mathematicae},
     volume = {158},
     year = {1998},
     pages = {69-80},
     zbl = {0912.55007},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv158i1p69bwm}
}

Mardešić, Sibe. Coherent and strong expansions of spaces coincide. Fundamenta Mathematicae, Tome 158 (1998) pp. 69-80. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv158i1p69bwm/

[00000] [G] B. Günther, Comparison of the coherent pro-homotopy theories of Edwards-Hastings, Lisica-Mardešić and Günther, Glas. Mat. 26 (1991), 141-176. | Zbl 0795.55010

[00001] [LM1] Ju. T. Lisica and S. Mardešić, Steenrod-Sitnikov homology for arbitrary spaces, Bull. Amer. Math. Soc. 9 (1983), 207-210. | Zbl 0532.55003

[00002] [LM2] Ju. T. Lisica and S. Mardešić, Coherent prohomotopy and strong shape category of topological spaces, in: Proc. Internat. Topology Conference (Leningrad, 1982), Lecture Notes in Math. 1060, Springer, Berlin, 1984, 164-173.

[00003] [LM3] Ju. T. Lisica and S. Mardešić, Coherent prohomotopy and strong shape theory, Glas. Mat. 19 (39) (1984), 335-399.

[00004] [M1] S. Mardešić, Approximate polyhedra, resolutions of maps and shape fibrations, Fund. Math. 114 (1981), 53-78. | Zbl 0411.54019

[00005] [M2] S. Mardešić, Strong expansions and strong shape theory, Topology Appl. 38 (1991), 275-291. | Zbl 0715.55008

[00006] [M3] S. Mardešić, Resolutions of spaces are strong expansions, Publ. Inst. Math. Beograd 49 (63) (1991), 179-188. | Zbl 0774.54015

[00007] [M4] S. Mardešić, Strong expansions and strong shape for pairs of spaces, Rad Hrvat. Akad. Znan. Umjetn. Matem. Znan. 456 (10) (1991), 159-172. | Zbl 0790.54019

[00008] [M5] S. Mardešić, Coherent homotopy and localization, Topology Appl. (1998) (to appear).

[00009] [MS] S. Mardešić and J. Segal, Shape Theory - The Inverse System Approach, North-Holland, Amsterdam, 1982. | Zbl 0495.55001

[00010] [T] H. Thiemann, Strong shape and fibrations, Glas. Mat. 30 (1995), 135-174. | Zbl 0870.55007

[00011] [V] R. M. Vogt, A note on homotopy equivalences, Proc. Amer. Math. Soc. 32 (1972), 627-629. | Zbl 0241.55009