sets in ANR's
Author:
David W. Henderson
Journal:
Trans. Amer. Math. Soc. 213 (1975), 205216
MSC:
Primary 54C55; Secondary 57A20
MathSciNet review:
0391008
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Abstract 
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Abstract: (1) Let A be a closed Zset in an ANR X. Let be an open cover of X. Then there is a homotopy inverse to the inclusion such that f and both homotopies are limited by . (2) If, in addition, X is a manifold modeled on a metrizable locally convex TVS, F, such that F is homeomorphic to , then there is a homotopy limited by such that the closure (in X) of is contained in .
 [1]
R.
D. Anderson, On topological infinite deficiency, Michigan
Math. J. 14 (1967), 365–383. MR 0214041
(35 #4893)
 [2]
R.
D. Anderson, David
W. Henderson, and James
E. West, Negligible subsets of infinitedimensional manifolds,
Compositio Math. 21 (1969), 143–150. MR 0246326
(39 #7630)
 [3]
Karol
Borsuk, Theory of retracts, Monografie Matematyczne, Tom 44,
Państwowe Wydawnictwo Naukowe, Warsaw, 1967. MR 0216473
(35 #7306)
 [4]
T.
A. Chapman, Deficiency in infinitedimensional manifolds,
General Topology and Appl. 1 (1971), 263–272. MR 0322898
(48 #1259)
 [5]
C.
H. Dowker, Mapping theorems for noncompact spaces, Amer. J.
Math. 69 (1947), 200–242. MR 0020771
(8,594g)
 [6]
K.
H. Dauker, Affine and euclidean complexes, Dokl. Akad. Nauk
SSSR 128 (1959), 655–656 (Russian). MR 0117708
(22 #8483)
 [7]
James
Dugundji, Topology, Allyn and Bacon, Inc., Boston, Mass.,
1966. MR
0193606 (33 #1824)
 [8]
James
Eells Jr. and Nicolaas
H. Kuiper, Homotopy negligible subsets, Compositio Math.
21 (1969), 155–161. MR 0253331
(40 #6546)
 [9]
R.
Engelking, Outline of general topology, Translated from the
Polish by K. Sieklucki, NorthHolland Publishing Co., Amsterdam; PWNPolish
Scientific Publishers, Warsaw; Interscience Publishers Division John Wiley
& Sons, Inc., New York, 1968. MR 0230273
(37 #5836)
 [10]
A.
M. Gleason, Spaces with a compact Lie group of
transformations, Proc. Amer. Math. Soc. 1 (1950), 35–43. MR 0033830
(11,497e), http://dx.doi.org/10.1090/S00029939195000338307
 [11]
Richard
E. Heisey, Manifolds modelled on
𝑅^{∞} or bounded weak*\ topologies, Trans. Amer. Math. Soc. 206 (1975), 295–312. MR 0397768
(53 #1626), http://dx.doi.org/10.1090/S0002994719750397768X
 [12]
David
W. Henderson, Corrections and extensions of two papers about
infinitedimensional manifolds, General Topology and Appl.
1 (1971), 321–327. MR 0293677
(45 #2754)
 [13]
David
W. Henderson, Stable classification of infinitedimensional
manifolds by homotopytype, Invent. Math. 12 (1971),
48–56. MR
0290413 (44 #7594)
 [14]
David
W. Henderson, Microbundles with infinitedimensional fibers are
trivial, Invent. Math. 11 (1970), 293–303. MR 0282380
(43 #8092)
 [15]
J.
L. Kelley and Isaac
Namioka, Linear topological spaces, With the collaboration of
W. F. Donoghue, Jr., Kenneth R. Lucas, B. J. Pettis, Ebbe Thue Poulsen, G.
Baley Price, Wendy Robertson, W. R. Scott, Kennan T. Smith. The University
Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.,
1963. MR
0166578 (29 #3851)
 [16]
W. K. Mason, Deficiency in spaces of homeomorphisms (to appear).
 [17]
R.
Schori, Topological stability for infinitedimensional
manifolds, Compositio Math. 23 (1971), 87–100.
MR
0287586 (44 #4789)
 [18]
H. Torunczyk, (G, K)skeleton and absorbing sets in complete metric spaces, Fund. Math. (to appear).
 [1]
 R. D. Anderson, On topological infinite deficiency, Michigan Math. J. 14 (1967), 365383. MR 35 #4893. MR 0214041 (35:4893)
 [2]
 R. D. Anderson, D. W. Henderson and J. E. West, Negligible subsets of infinitedimensional manifolds, Compositio Math. 21 (1969), 143150. MR 39 #7630. MR 0246326 (39:7630)
 [3]
 K. Borsuk, Theory of retracts, Monografie Mat., tom 44, PWN, Warsaw, 1967. MR 35 #7306. MR 0216473 (35:7306)
 [4]
 T. A. Chapman, Deficiency in infinitedimensional manifolds, General Topology and Appl. 1 (1971), 263272. MR 48 #1259. MR 0322898 (48:1259)
 [5]
 C. H. Dowker, Mapping theorems for noncompact spaces, Amer. J. Math. 69 (1947), 200242. MR 8, 594. MR 0020771 (8:594g)
 [6]
 , On affine and euclidean complexes, Dokl. Akad. Nauk SSSR 128 (1959), 655656. (Russian) MR 22 #8483. MR 0117708 (22:8483)
 [7]
 J. Dugundji, Topology, Allyn and Bacon, Boston, Mass., 1966. MR 33 #1824. MR 0193606 (33:1824)
 [8]
 J. Eells, Jr. and N. H. Kuiper, Homotopy negligible subsets, Compositio Math. 21 (1969), 155161. MR 40 #6546. MR 0253331 (40:6546)
 [9]
 R. Engelking, Outline of general topology, PWN, Warsaw, 1965; English transl., NorthHolland, Amsterdam; Interscience, New York, 1968. MR 36 #4508; 37 #5836. MR 0230273 (37:5836)
 [10]
 A. M. Gleason, Spaces with a compact Lie group of transformations, Proc. Amer. Math. Soc. 1 (1950), 3543. MR 11, 497. MR 0033830 (11:497e)
 [11]
 R. Heisey, Manifolds modelled on or bounded weak topologies, Trans. Amer. Math. Soc. 206 (1975), 295312. MR 0397768 (53:1626)
 [12]
 D. W. Henderson, Corrections and extensions of two papers about infinitedimensional manifolds, General Topology and Appl. 1 (1971), 321327. MR 45 #2754. MR 0293677 (45:2754)
 [13]
 , Stable classification of infinitedimensional manifolds by homotopytype Invent. Math. 12 (1971), 4856. MR 44 #7594. MR 0290413 (44:7594)
 [14]
 , Microbundles with infinitedimensional fibers are trivial, Invent. Math. 11 (1970), 293303. MR 43 #8092. MR 0282380 (43:8092)
 [15]
 J. Kelley, I. Namioka et al., Linear topological spaces, University Ser. in Higher Math., Van Nostrand, Princeton, N. J., 1963. MR 29 #3851. MR 0166578 (29:3851)
 [16]
 W. K. Mason, Deficiency in spaces of homeomorphisms (to appear).
 [17]
 R. M. Schori, Topological stability for infinitedimensional manifolds, Compositio Math. 23 (1971), 87100. MR 44 #4789. MR 0287586 (44:4789)
 [18]
 H. Torunczyk, (G, K)skeleton and absorbing sets in complete metric spaces, Fund. Math. (to appear).
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197503910083
PII:
S 00029947(1975)03910083
Article copyright:
© Copyright 1975
American Mathematical Society
