The Kuratowski-Dugundji theorem that a metrizable space is an absolute (neighborhood) extensor in dimension n iff it is (resp., ) is extended to a class of non-metrizable absolute (neighborhood) extensors in dimension n. On this base, several facts concerning metrizable extensors are established for non-metrizable ones.
@article{bwmeta1.element.bwnjournal-article-fmv145i3p243bwm, author = {Valentin Gutev and Vesko Valov}, title = {Classical-type characterizations of non-metrizable ANE(n)-spaces}, journal = {Fundamenta Mathematicae}, volume = {144}, year = {1994}, pages = {243-259}, zbl = {0811.54020}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv145i3p243bwm} }
Gutev, Valentin; Valov, Vesko. Classical-type characterizations of non-metrizable ANE(n)-spaces. Fundamenta Mathematicae, Tome 144 (1994) pp. 243-259. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv145i3p243bwm/
[00000] [1] A. Chigogidze, Noncompact absolute extensors in dimension n, n-soft mappings, and their applications, Izv. Akad. Nauk SSSR 50 (1) (1986), 156-180 (in Russian); English transl.: Math. USSR-Izv. 28 (1987), 151-174. | Zbl 0603.54018
[00001] [2] A. Dranishnikov, Absolute extensors in dimension n and dimension-raising n-soft maps, Uspekhi Mat. Nauk 39 (5) (1984), 55-95 (in Russian); English transl.: Russian Math. Surveys 39 (1984). | Zbl 0572.54012
[00002] [3] J. Dugundji, Absolute neighborhood retracts and local connectedness in arbitrary metric spaces, Compositio Math. 13 (1958), 229-246. | Zbl 0089.38903
[00003] [4] V. Filippov, On the dimension of products of topological spaces, Fund. Math. 106 (1980), 181-212 (in Russian). | Zbl 0464.54042
[00004] [5] V. Gutev, Selections for quasi-l.s.c. mappings with uniformly equi- range, Set-Valued Anal. 1 (1993), 319-328. | Zbl 0809.54016
[00005] [6] R. Haydon, On a problem of Pełczyński: Milutin spaces, Dugundji spaces and AE(0-dim), Studia Math. 52 (1974), 23-31. | Zbl 0294.46016
[00006] [7] K. Kuratowski, Sur les espaces localement connexes et péaniens en dimension n, Fund. Math. 24 (1935), 269-287. | Zbl 0011.04002
[00007] [8] E. Michael, Continuous selections II, Ann. of Math. 64 (1956), 562-580. | Zbl 0073.17702
[00008] [9] R. Pol and E. Puzio-Pol, Remarks on Cartesian products, Fund. Math. 93 (1976), 57-69.
[00009] [10] E. V. Ščepin [E. V. Shchepin], Functors and uncountable powers of compacta, Uspekhi Mat. Nauk 36 (3) (1981), 3-62 (in Russian); English transl.: Russian Math. Surveys 36 (1981). | Zbl 0463.54009
[00010] [11] L. Shirokov, On AE(n)-compacta and n-soft mappings, Sibirsk. Mat. Zh. 33 (1992), 151-156 (in Russian). | Zbl 0873.54020
[00011] [12] H. Toruńczyk, Concerning locally homotopy negligible sets and characterizations of -manifolds, Fund. Math. 101 (1978), 93-110. | Zbl 0406.55003
[00012] [13] V. Valov, Another characterization of AE(0)-spaces, Pacific J. Math. 127 (1987), 199-208. | Zbl 0593.54033