A metric space (X,ϱ) satisfies the disjoint (0,n)-cells property provided for each point x ∈ X, any map f of the n-cell into X and for each ε > 0 there exist a point y ∈ X and a map such that ϱ(x,y) < ε, and . It is proved that each homogeneous locally compact ANR of dimension >2 has the disjoint (0,2)-cells property. If dimX = n > 0, X has the disjoint (0,n-1)-cells property and X is a locally compact -space then local homologies satisfy for k < n and Hn(X,X-x) ≠ 0.
@article{bwmeta1.element.bwnjournal-article-cmv66i1p77bwm, author = {Pawe\l\ Krupski}, title = {On the disjoint (0,N)-cells property for homogeneous ANR's}, journal = {Colloquium Mathematicae}, volume = {66}, year = {1993}, pages = {77-84}, zbl = {0849.54026}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv66i1p77bwm} }
Krupski, Paweł. On the disjoint (0,N)-cells property for homogeneous ANR's. Colloquium Mathematicae, Tome 66 (1993) pp. 77-84. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv66i1p77bwm/
[000] [1] R. H. Bing and K. Borsuk, Some remarks concerning topologically homogeneous spaces, Ann. of Math. 81 (1965), 100-111. | Zbl 0127.13302
[001] [2] K. Borsuk, Theory of Retracts, PWN-Polish Sci. Publ., Warszawa, 1967. | Zbl 0153.52905
[002] [3] J. J. Charatonik and T. Maćkowiak, Around Effros' theorem, Trans. Amer. Math. Soc. 298 (1986), 579-602. | Zbl 0608.54012
[003] [4] R. J. Daverman, Detecting the disjoint disks property, Pacific J. Math. 93 (1981), 277-298. | Zbl 0415.57007
[004] [5] R. J. Daverman, Decompositions of Manifolds, Academic Press, Orlando, 1986. | Zbl 0608.57002
[005] [6] P. Krupski, Homogeneity and Cantor manifolds, Proc. Amer. Math. Soc. 109 (1990), 1135-1142. | Zbl 0714.54035
[006] [7] P. Krupski, Recent results on homogeneous curves and ANR's, Topology Proc. 16 (1991), 109-118. | Zbl 0801.54015
[007] [8] J. M. Łysko, On homogeneous ANR-spaces, in: Proc. Internat. Conf. on Geometric Topology, PWN-Polish Sci. Publ., Warszawa, 1980, 305-306.
[008] [9] J. van Mill, Infinite-Dimensional Topology, North-Holland, Amsterdam, 1989.
[009] [10] W. J. R. Mitchell, General position properties of ANR's, Math. Proc. Cambridge Philos. Soc. 92 (1982), 451-466. | Zbl 0529.57008
[010] [11] E. H. Spanier, Algebraic Topology, McGraw-Hill, New York, 1966.