Weak homotopy equivalences of mapping spaces and Vogt's lemma

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1. [1] S.A. Antonyan, Mapping spaces are equivariant absolute extensors, Vestnik Moskov. Univ. Ser. I, Mat. Mekh. (1981), 22-25. Zbl0478.54012MR648583
2. [2] S.A. Antonyan and S. Mardešić, Equivariant shape, Fund. Math. 127 (1987), 213-224. Zbl0644.55009MR917146
3. [3] S.A. Antonyan, Retraction properties of an orbit spaces. II (Russian), Uspekhi Mat. Nauk 48 (1993), no. 6(294), 145-146; translation in Russian Math. Surveys 48 (1993), no. 6. 156-157. Zbl0832.54019MR1264160
4. [4] S.A. Antonyan, A characterization of equivariant absolute extensors and the equivarian Dugundji Theorem, Houston J. Math. Vol 31, No. 2 (2000), 451-462. Zbl1103.54011MR2132847
5. [5] S.A. Antonyan and E. Elfving, The equivariant homotopy type of G-ANR'S for compact group actions. Dubrovnik VI - Geométrie Topology 2007, http://atlas-conferences.eom/c/a/u/w/64.htm. Zbl1134.55008
6. [6] R. Brown, Topology, Ellis Horwood (1988). Zbl0655.55001MR984598
7. [7] C. Casacuberta and J.L. Rodriguez, On weak honotopy equivalences between mapping spaces, Topology vol. 37, no. 4 (1998), 709-717. Zbl0897.55006MR1607716
8. [8] J.-M. Cordier and T. Porter, Categorical shape theory, World Scientific (1996). 
9. [9] D. Deleanu and P.J. Hilton, On the categorical shape of functors, Fund. Math. 97 (1977), 157-176. Zbl0368.18002MR645375
10. [10] E.D. Dubuc, Kan Extension in Enriched Category Theory, Lecture Notes in Math. 145, Springer-Verlag, Berlin-Heidelberg-New York (1970). Zbl0228.18002MR280560
11. [11] J. Dydak and S. Nowak, Strong shape for topological spaces, Trans. Amer. Math. Soc. 323(2) (1991), 765-796. Zbl0754.55009MR986690
12. [12] J. Dydak and S. Nowak, Function spaces and shape theories, Fund. Math. 171 (2002), 117-154. Zbl0989.55008MR1880380
13. [13] P.H.H. Fantham, E.J. Moore, Groupoid enriched categories and homotopy theory, Canad. J. Math. 3 (1983), 385-416. Zbl0546.55026MR717131
14. [14] A. Frei, On categorical shape theory, Cahiers Topologie Géom. Différentialle Catég. 17 (3) (1976), 261-294. Zbl0341.55015MR439911
15. [15] A. Gaszak, The Whitehead theorem in equivariant shape theory, Glasnik Mat. 234 (44) (1989), 417-425. Zbl0711.54009MR1074884
16. [16] P.S. Gevorgyan, Some questions of equivariant movability, Glasnik Mat. vol. 39 (59) (2004), 185-198. Zbl1053.55006MR2055395
17. [17] P.J. Higgins, Categories and Groupoids, Van Nostrand Reinhold Math. St., vol. 32 (1971). Zbl0226.20054MR327946
18. [18] P.S. Hirschorn, Localization of Model Categories, Mathematical Surveys and Monographs 99, Am. Math. Soc., Providence, RI (2003). Zbl1017.55001
19. [19] R. Lashof, The immersion approach to triangulation and smooothing, Proc. Adv. St. on Alg. Top., Aarhus Universitet (1970). Zbl0236.57010MR281212
20. [20] S. Mardešić, Strong Shape and Homology, Springer Monographs in Mathematics, Springer Verlag, Berlin-Heidelberg-New York (2000). Zbl0939.55007MR1740831
21. [21] T. Matumoto, Equivariant CW complexes and shape theory, Tsukuba J. Math. vol. 1 (1989), 157-164. Zbl0683.55005MR1003599
22. [22] I. Pop, An equivariant shape theory, An. Stint. Univ. "Al. I. Cuza" Iaşi, s. la (1984), 53-67. Zbl0559.55014MR777027
23. [23] L. Stramaccia, Groupoids and strong shape, Topology and Appl. 153 (2005), 528-539. Zbl1083.55008MR2175367
24. [24] L. Stramaccia, 2-Categorical aspect of strong shape, Topology and Appl. 153 (2006), 3007-3018. Zbl1100.54012MR2248404
25. [25] R. Vogt, A note on homotopy equivalences, Proc. Amer. Math. Soc. 32 (1972), 627-629. Zbl0241.55009MR293632
26. [26] G.W. Whitehead, Elements of Homotopy Theory, Springer-Verlag, New York, Heidelberg, Berlin (1978). Zbl0406.55001MR516508