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Homotopy properties of decomposition spaces
Author:
Steve Armentrout
Journal:
Trans. Amer. Math. Soc. 143 (1969), 499-507
MSC:
Primary 54.55; Secondary 55.00
MathSciNet review:
0273574
Full-text PDF Free Access
References |
Similar Articles |
Additional Information
- [1]
Steve
Armentrout, Upper semi-continuous decompositions of 𝐸³
with at most countably many non-degenerate elements, Ann. of Math. (2)
78 (1963), 605–618. MR 0156331
(27 #6255)
- [2]
Steve
Armentrout, Cellular decompositions of 3-manifolds
that yield 3-manifolds, Bull. Amer. Math.
Soc. 75 (1969),
453–456. MR 0239578
(39 #935), http://dx.doi.org/10.1090/S0002-9904-1969-12218-4
- [3]
Steve
Armentrout, 𝑈𝑉 properties of
compact sets, Trans. Amer. Math. Soc. 143 (1969), 487–498.
MR
0273573 (42 #8451), http://dx.doi.org/10.1090/S0002-9947-1969-0273573-7
- [4]
Steve
Armentrout and Thomas
M. Price, Decompositions into compact sets with
𝑈𝑉 properties, Trans. Amer.
Math. Soc. 141
(1969), 433–442. MR 0244994
(39 #6307), http://dx.doi.org/10.1090/S0002-9947-1969-0244994-3
- [5]
R.
H. Bing, A surface is tame if its complement is
1-ULC, Trans. Amer. Math. Soc. 101 (1961), 294–305. MR 0131265
(24 #A1117), http://dx.doi.org/10.1090/S0002-9947-1961-0131265-1
- [6]
Karol
Borsuk, Theory of retracts, Monografie Matematyczne, Tom 44,
Państwowe Wydawnictwo Naukowe, Warsaw, 1967. MR 0216473
(35 #7306)
- [7]
V.
P. Kompaniec and A.
V. Černavskiĭ, Equivalence of two classes of sphere
mappings, Soviet Math. Dokl. 7 (1966),
1083–1085. MR 0240788
(39 #2133)
- [8]
E.
H. Connell, A topological 𝐻-cobordism theorem for
𝑛≥5, Illinois J. Math. 11 (1967),
300–309. MR 0212808
(35 #3673)
- [9]
D.
M. Hyman, 𝐴𝑁𝑅 divisors and absolute
neighborhood contractability, Fund. Math. 62 (1968),
61–73. MR
0229197 (37 #4771)
- [10]
R.
C. Lacher, Cell-like mappings of
𝐴𝑁𝑅’𝑠, Bull. Amer. Math. Soc. 74 (1968), 933–935. MR 0244963
(39 #6276), http://dx.doi.org/10.1090/S0002-9904-1968-12093-2
- [11]
Joseph
Martin, The sum of two crumpled cubes, Michigan Math. J.
13 (1966), 147–151. MR 0190914
(32 #8324)
- [12]
D.
R. McMillan Jr., A criterion for cellularity in a manifold,
Ann. of Math. (2) 79 (1964), 327–337. MR 0161320
(28 #4528)
- [13]
T.
M. Price, A necessary condition that a cellular
upper semi-continuous decomposition of 𝐸ⁿ yield
𝐸ⁿ, Trans. Amer. Math. Soc.
122 (1966),
427–435. MR 0193627
(33 #1843), http://dx.doi.org/10.1090/S0002-9947-1966-0193627-0
- [14]
Stephen
Smale, A Vietoris mapping theorem for
homotopy, Proc. Amer. Math. Soc. 8 (1957), 604–610. MR 0087106
(19,302f), http://dx.doi.org/10.1090/S0002-9939-1957-0087106-9
- [15]
J. H. C. Whitehead, On the homotopy type of ANR's, Bull. Amer. Math. Soc. 55 (1949), 453-496.
- [1]
- S. Armentrout, Upper semi-continuous decompositions of
with at most countably many non-degenerate elements, Ann. of Math. 79 (1963), 605-618. MR 0156331 (27:6255)
- [2]
- -, Cellular decompositions of 3-manifolds that yield 3-manifolds, Bull. Amer. Math. Soc. 75 (1969), 453-455. MR 0239578 (39:935)
- [3]
- -, UV properties of compact sets, Trans. Amer. Math. Soc. 143 (1969), 487-498. MR 0273573 (42:8451)
- [4]
- S. Armentrout and T. M. Price, Decompositions into compact sets with UV properties, Trans. Amer. Math. Soc. 141 (1969), 433-442. MR 0244994 (39:6307)
- [5]
- R. H. Bing, A surface is tame if its complement is 1-ULC, Trans. Amer. Math. Soc. 101 (1961), 294-305. MR 0131265 (24:A1117)
- [6]
- K. Borsuk, Theory of retracts, Monogr. Mat., Vol. 44, Polish Scientific Publishers, Warsaw, 1967. MR 0216473 (35:7306)
- [7]
- A. V. Černavskiĭ and V. P. Kompaniec, Equivalence of two classes of sphere mappings, Soviet Math. 7 (1966), pp. 1083-1085. MR 0240788 (39:2133)
- [8]
- E. H. Connell, A topological h-cobordism theorem for
, Illinois J. Math. 11 (1967), 300-309. MR 0212808 (35:3673)
- [9]
- D. M. Hyman, ANR divisors and absolute neighborhood contractibility, Fund. Math. 62 (1968), 61-73. MR 0229197 (37:4771)
- [10]
- R. C. Lacher, Cell-like spaces and mappings, Bull. Amer. Math. Soc. 74 (1968), 933-935. MR 0244963 (39:6276)
- [11]
- J. Martin, The sum of two crumpled cubes, Michigan Math. J. 13 (1966), 147-151. MR 0190914 (32:8324)
- [12]
- D. R. McMillan, Jr., A criterion for cellularity in a manifold, Ann. of Math. 79 (1964), 327-337. MR 0161320 (28:4528)
- [13]
- T. M. Price, A necessary condition that a cellular upper semicontinuous decomposition of
yield , Trans. Amer. Math. Soc. 122 (1966), 427-435. MR 0193627 (33:1843)
- [14]
- S. Smale, A Vietoris mapping theorem for homotopy, Proc. Amer. Math. Soc. 8 (1957), 604-610. MR 0087106 (19:302f)
- [15]
- J. H. C. Whitehead, On the homotopy type of ANR's, Bull. Amer. Math. Soc. 55 (1949), 453-496.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9947-1969-0273574-9
PII:
S 0002-9947(1969)0273574-9
Article copyright:
© Copyright 1969 American Mathematical Society
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