×

zbMATH — the first resource for mathematics

Infinite-dimensional methods in finite-dimensional geometric topology. (English) Zbl 0256.57004

MSC:
57N15 Topology of the Euclidean \(n\)-space, \(n\)-manifolds (\(4 \leq n \leq \infty\)) (MSC2010)
57N20 Topology of infinite-dimensional manifolds
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] R. D. Anderson, Strongly negligible sets in Fréchet manifolds, Bull. Amer. Math. Soc. 75 (1969), 64 – 67. · Zbl 0195.53602
[2] R. D. Anderson, On sigma-compact subsets of infinite-dimensional spaces, Trans. Amer. Math. Soc. (to appear).
[3] C. Bessaga and A. Pełczyński, The estimated extension theorem, homogeneous collections and skeletons, and their applications to the topological classification of linear metric spaces and convex sets, Fund. Math. 69 (1970), 153 – 190. · Zbl 0204.12801
[4] R. H. Bing, Locally tame sets are tame, Ann. of Math. (2) 59 (1954), 145 – 158. · Zbl 0055.16802 · doi:10.2307/1969836 · doi.org
[5] R. H. Bing and J. M. Kister, Taming complexes in hyperplanes, Duke Math. J. 31 (1964), 491 – 511. · Zbl 0124.16701
[6] H. G. Bothe, Eine Einbettung \?-dimensionaler Mengen in einen (\?+1)-dimensionalen absoluten Retrakt, Fund. Math. 52 (1963), 209 – 224 (German). · Zbl 0113.38002
[7] J. L. Bryant, On embeddings of compacta in Euclidean space, Proc. Amer. Math. Soc. 23 (1969), 46 – 51. · Zbl 0186.57701
[8] J. L. Bryant, On embeddings of 1-dimensional compacta in \?\(^{5}\), Duke Math. J. 38 (1971), 265 – 270. · Zbl 0224.54011
[9] A. V. Černavskiĭ, Topological embeddings of manifolds, Dokl. Akad. Nauk SSSR 187 (1969), 1247 – 1250 (Russian).
[10] Herman Gluck, Embeddings in the trivial range, Ann. of Math. (2) 81 (1965), 195 – 210. · Zbl 0134.42904 · doi:10.2307/1970614 · doi.org
[11] R. Kirby, Lectures on triangulations of manifolds, Mimeographed notes, University of California, Los Angeles, Calif., 1969.
[12] D. R. McMillan Jr., Taming Cantor sets in \?\(^{n}\), Bull. Amer. Math. Soc. 70 (1964), 706 – 708. · Zbl 0122.18101
[13] K. Menger, Über umfassendste n-dimensionale Mengen, Nederl. Akad. Wetensch. Proc. Ser. A 29 (1926), 1125-1128. · JFM 52.0595.01
[14] T. Rado, Über den Begriff der Riemannschen Fläche, Acta Sci. Math. Szeged. 2 (1925), 101-121. · JFM 51.0273.01
[15] T. B. Rushing, Taming codimension three embeddings, Bull. Amer. Math. Soc. 75 (1969), 815 – 820. · Zbl 0176.22001
[16] M. A. Štan\(^{\prime}\)ko, Imbedding of compacta in euclidean space, Mat. Sb. (N.S.) 83 (125) (1970), 234 – 255 (Russian).
[17] M. A. Štan\(^{\prime}\)ko, Solution of Menger’s problem in the class of compacta, Dokl. Akad. Nauk SSSR 201 (1971), 1299 – 1302 (Russian).
[18] H. Toruńczyk, Skeletonized sets in complete metric spaces and homeomorphisms of the Hilbert cube, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 18 (1970), 119 – 126 (English, with Loose Russian summary). · Zbl 0202.54003
[19] James E. West, The ambient homeomorphy of an incomplete subspace of infinite-dimensional Hilbert spaces, Pacific J. Math. 34 (1970), 257 – 267. · Zbl 0198.46001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.