THE PRODUCT OF SHAPE FIBRATIONS

Year 2013, Volume: 1 Issue: 2, 103 - 111, 01.12.2013

Qamil Haxhibeqiri Qamil Haxhıbeqırı

https://izlik.org/JA25EY39TD

Abstract

The following fact is shown: Let p : E → B, p : E→ B bemaps of compact Hausdorff spaces. Then p × p : E × E → B × B is a shapefibration if and only if p and p are shape fibrations.Also the following fact onresolutions is shown:Let q = (qλ) : E → E = (Eλ, qλλ, Λ) and r = (rµ) : B → B = (Bµ, rµµ, M )are morphisms of pro-Cpt such that E and B are compact AN R-systems.Then q × r = (qλ× rµ) : E × B → E × B = (Eλ× Bµ, qλλ× rµµ, Λ × M )is a resolution of E × B if and only if q and r are resolutions of E and B,respectively. (Theorem 1)

Keywords

Shape fibrations , resolution , approximate homotopy lifting property

References

• Haxhibeqiri,Q., Shape fibrations for topological spaces, Glas. Mat. 17 (37) (1982), pp. 381- 401. [2] Haxhibeqiri,Q., The exact sequence of a shape fibration, Glas. Mat. 18 (38) (1983), pp. 157 - 177.
• Haxhibeqiri,Q., Shape fibrations for compact Hausdorff spaces, Publications de l’Inst. de Mat´em. 31(45) (1982), pp.33-49.
• Haxhibeqiri,Q., On the surjectivity of shape fibration, Matem. Vesnik, 37 (1985),pp.379- 384. [5] Mardeˇsi´c, S., Approximate polyhedra, resolutions of maps and shape fibrations, Fund. Math. 114 (1981), pp. 53-78.
• Mardeˇsi´c, S., On resolutions for pairs of spaces, Tsukuba J. Math. Vol. 8, No. 1(1984), pp.81- 93. [7] Mardeˇsi´c, S., The foundations of shape theory, Lecture Notes, Univ. of Kentucky, 1978.
• Mardeˇsi´c, S. and Rushing, T,. Shape fibrations I, Gen.Top. and Appl. 9(1978), pp. 193 - 215. [9] Mardeˇsi´c, S. and Rushing, T,. Shape fibrations II, Gen.Top. and Appl. 9(1979), pp. 283 -298. [10] Mardeˇsi´c, S. and Segal, J., Shape theory, North-Holland Pub.Comp., Amsterdam, 1982.
• Mardeˇsi´c, S. and Watanabe, T., Approximate resolutions of spaces and mappings, Glas.Mat. 24 (44)(1989), 587 - 637.
• Lisica, Ju. and Mardeˇsi´c, S., Coherent prohomotopy and strong shape theory, Glas. Mat. 19 (39) (1984), pp. 335 - 399.
• Spanier, E., Algebraic Topology, McGraw-Hill book Comp., New-York, 1966.
• Watanabe, T., Approximative shape theory, Mimeographed Notes,Univ. of Yamaguchi, 1982. [15] Watanabe, T., Approximative shape theory I, Tsukuba J. Math. Vol.11, No. 1 (1987), pp.17- 59. Prishtin¨e-KOSOV/”E
• E-mail address: [e-mail]