Cells and cellularity in infinite-dimensional normed linear spaces

McCoy, R. A.

doi:10.1090/S0002-9947-1973-0383419-5

Cells and cellularity in infinite-dimensional normed linear spaces
HTML articles powered by AMS MathViewer

by R. A. McCoy PDF

Trans. Amer. Math. Soc. 176 (1973), 401-410 Request permission

Abstract:

Certain concepts such as cells, cellular sets, point-like sets, and decomposition spaces are studied and related in normed linear spaces. The relationships between these concepts in general resemble somewhat the corresponding relationships in Euclidean space.

References

R. D. Anderson, Topological properties of the Hilbert cube and the infinite product of open intervals, Trans. Amer. Math. Soc. 126 (1967), 200–216. MR 205212, DOI 10.1090/S0002-9947-1967-0205212-3
R. D. Anderson, On topological infinite deficiency, Michigan Math. J. 14 (1967), 365–383. MR 214041
R. D. Anderson and R. H. Bing, A complete elementary proof that Hilbert space is homeomorphic to the countable infinite product of lines, Bull. Amer. Math. Soc. 74 (1968), 771–792. MR 230284, DOI 10.1090/S0002-9904-1968-12044-0
R. D. Anderson, David W. Henderson, and James E. West, Negligible subsets of infinite-dimensional manifolds, Compositio Math. 21 (1969), 143–150. MR 246326
Karol Borsuk, Concerning homotopy properties of compacta, Fund. Math. 62 (1968), 223–254. MR 229237, DOI 10.4064/fm-62-3-223-254
Karol Borsuk, Fundamental retracts and extensions of fundamental sequences, Fund. Math. 64 (1969), 55-85; errata, ibid. 64 (1969), 375. MR 0243520, DOI 10.4064/fm-64-1-55-85
Karol Borsuk, A note on the theory of shape of compacta, Fund. Math. 67 (1970), 265–278. MR 266169, DOI 10.4064/fm-67-2-265-278
Morton Brown, The monotone union of open $n$-cells is an open $n$-cell, Proc. Amer. Math. Soc. 12 (1961), 812–814. MR 126835, DOI 10.1090/S0002-9939-1961-0126835-6
T. A. Chapman, On some applications of infinite-dimensional manifolds to the theory of shape, Fund. Math. 76 (1972), no. 3, 181–193. MR 320997, DOI 10.4064/fm-76-3-181-193
D. W. Curtis and R. A. McCoy, Stable homeomorphisms on infinite-dimensional normed linear spaces, Proc. Amer. Math. Soc. 28 (1971), 496–500. MR 283831, DOI 10.1090/S0002-9939-1971-0283831-2
William H. Cutler, Negligible subsets of infinite-dimensional Fréchet manifolds, Proc. Amer. Math. Soc. 23 (1969), 668–675. MR 248883, DOI 10.1090/S0002-9939-1969-0248883-5
Charles Greathouse, Locally flat strings, Bull. Amer. Math. Soc. 70 (1964), 415–418. MR 161318, DOI 10.1090/S0002-9904-1964-11122-8
David W. Henderson and R. Schori, Topological classification of infinite dimensional manifolds by homotopy type, Bull. Amer. Math. Soc. 76 (1970), 121–124. MR 251749, DOI 10.1090/S0002-9904-1970-12392-8
V. L. Klee Jr., A note on topological properties of normed linear spaces, Proc. Amer. Math. Soc. 7 (1956), 673–674. MR 78661, DOI 10.1090/S0002-9939-1956-0078661-2
D. E. Sanderson, An infinite-dimensional Schoenflies theorem, Trans. Amer. Math. Soc. 148 (1970), 33–39. MR 259957, DOI 10.1090/S0002-9947-1970-0259957-X