Annals of the New York Academy of Sciences 1996: Vol 788 Index

5 Pages·1996·0.39 MB·English

Subject Index
■A^belian (see group, semigroup) compactness
absolute, 13,14, 32 almost stable local, 40, 45
absolute neighborhood retracts, 214 joint, 40, 43, 44, 48
absolutely, 203 pairwise, 40, 43
stable, 40, 45
completely regular subspace, 9-11
Baire set, 209
component, 108, 118, 119
Baire space, 96-98,125, 197-200, 202
nondegenerate, 118
Banach space, 9, 12,185, 186
identity of Z(G) and of Zq(N), 138
Banach-Stone theorem, 9,11
connected space, 108
^N, 124-127
continuum, hereditarily indecomposable,
bitopology, 40
108, 119
biweight, 40, 45
indecomposable, 108, 118
Boolean subalgebra, 80
countable tightness, 203-205,207, 208
Borel (Baire) group, 95
countably compact, 124-131
Borel set, 95, 96,99, 100
locally, 124
cozero-set, 101-104
Cardinality, 40, 44, 45, 48, 51-53, 134, cut point, 170
135, 161,191,197, 200-202
maximal, 180
Dendritic space, 170-174
cellularity, 197, 198, 200
dendron, 170-174
compact, 13, 45, 48, 79, 80, 93, 94, 108,
disjoint families, almost, 147,159
114, 122, 146, 197, 203-205
almost stably locally, 40, 41, 44-46
absolutely countably, 203, 208
H/ssential maps, 175,176,183
countably, 137,203-206, 208
extremely disconnected space, 115, 126,
group, 138-146
127, 131,209,210,213
center of a, 138,143
locally, 40, 41, 43, 44, 96, 97, 118,
119, 147-152, 158, 192, Filter (base), 160,161
195, 219, 220 finite-to-one maps, 175,183
compact connected, 117 flows, 13-15, 18, 19, 21, 23, 24, 26, 28,
Abelian subgroup, 138,141,143-146 29, 31, 32
compact normal subgroup, centralizer of a, compact, 31
138, 139,142, 143 forcing, 79, 87, 88, 90, 91, 93, 94
compact separable sequential space, 81 forcing-notion Q, 86
compact sequential space, 79, 91, 94 Frechet-Urysohn space, 79, 93
compactification /-ring, 108, 119,121,123
Alexander, 211 1-convex, 108,110,112-114,121
Alexandroff, 9 archimedean semiprime, 112
dendritic, 172,173 semiprime, 108, 110, 111, 119, 121,
one-point, 75, 79, 80, 90,92, 93,116, 122
176 F-space, 108-111, 113-115, 117-120,
Stone-Cech, 28-30,33,106,108,110, 122
111, 122, 123, 160, 197, zero-dimensional, 113,115, 116, 120
198 function, proper multivalued, 57-60
Wallman, 160, 161 funnel, 69-71, 77
223
224 ANNALS NEW YORK ACADEMY OF SCIENCES
Crlicksberg’s theorem, 34, 38 locally finite collection, 54, 55
group lower semicontinuous maps, 184
Abelian, 164, 165, 188, 189, 191, Luzin gap, 147, 152, 155
195,201,218 strong, 154,155
(see also topological group)
Mad family, 79, 81, 83-85
Hilbert cube, 214, 217 maximal protorus, 138, 140, 144
Holsztyhski’s theorem, 9,10 normalizerof the, 138, 143
homeomorphism
finite-dimensional, 214 Network, 54-56
space of, 214 nuclear group, 34, 35, 37, 39
homogeneous, 95-100
homotopic, properly, 57,59,62-66 (O-bounded, 203, 204, 207
open bases and networks, generalization
Ideal of, 133-136
maximal, 108,114, 121, 122
minimal prime, 108, 114, 116, 121, 7^2 space, 147, 152,159
122 paraconvex sets, 184,187
prime, 108, 121, 122 paratopological group, 125,127
inductive limit topology, 188-192 perfect map, 54, 55
infinite-dimensional, strongly, 175-178, periodic point, 69, 71, 72, 74, 75
183 plane, 69, 74, 76-78
intermediate value theorem (IVT), 108, projective cover, 13-15, 17, 18, 21, 22,
109, 111, 112,115, 117, 121 24-27,29, 30,32
ring, 108, 109, 111-116,122 proper multinet, 57,59, 60, 62
strong, 108,119 proper a-homotopy, 57
weak, 121 properly A/®-movable, 57
space, 108, 109, 111, 113, 115-119 properly M^-tame, 57, 61-63
strong, 108,119, 120 properly o-homotopic 66
weak, 121 property A, 101, 102,104-106
invariant measure, 218-222 pseudobicharacter, 40
inverse-closed subring, 101,102, 104 pseudocharacter, 40, 48
isometry, linear, 9-11 pseudocompact, 126-131, 197, 199-202
pseudocompact space, 197
pseudocompact topological group, 197
Jordan curve theorem, 69, 75
nondiscrete, 198
pseudocomplete, 197, 198, 200, 201
K
-fields of sets, 209 space, 199,202
pseudo-tree, 170-172,174
I^ightly compact, 197-199, 201
neighborhood, 199 Realcompactification, Hewitt-Nachbin,
space, 197,198, 200, 202 106
Lindelof space, 104,105, 108, 120 real-valued measurable cardinal, 218
Lindelof subset, 211 regionally proximal relation, 164
locally compact Abelian (lea) group, 34, regular point, 69, 71, 75
35, 38, 39 restorative, 133
locally compact semigroup, 164,165,168 R-tree, 170,171,173, 174
SUBJECT INDEX 225
Selected accumulation, base for, 133,134 topological group — continued
selections, 184 uncountable, 218
continuous, 185,187 zero-dimensional, 95
single-valued continuous, 185 topological semigroup, cancellative, 124-
semidynamical system, 69, 70, 77,78 131
semiflow, 69-71, 77 topological transformation semigroup, 164
semigroup. Abelian sub-, 125 trajectory, 69, 70, 72-76
semistratifiable space, developability of, Tychonoff plank, 125,127,130
133,136 Tychonoff space, 13, 109, 110, 111, 114,
sequential, 79-81, 91, 93, 94 116,119,121,164,168
space, 203, 204, 206
o-compact, 95-99, 118,119
a-relatively discrete, 54 Ultrafilter, 188,192,210,211, 221
o-small, 57 uniform closure, 101,105-107
starlike sets, 184
Stone space, 80, 210-212
SV-space, 108 V aluation domain, 108, 121, 123
adge class, 95,96
Two-manifold, 69-71, 77
Borel, 96
0-regularity, 160,162
weak reflection, 160-163
topological group, 29, 30,95, 97-99,124-
weak-[a)j, -oo)'' refinability
126, 128,-130, 139, 140, 166,
weight, 40, 45, 46
201,218,219
compact, 138-146
connected, 138 Zero-dimensional, 97, 100, 108, 109,
free, 164, 165, 169, 188-190, 195, 111, 113-118, 120, 150, 178,
196 179, 182
locally compact, 127 strongly, 108, 113,115,116, 120
pseudocompact, 197, 198, 200 Z-set, 214-216

Index of Contributors
A.arts, J.M., ix IN^artinez, J., 108
Araujo, J., 9 Martm-Peinador, E., 34
Maurice, M.A., ix
Megrelishvili (Levy), M., 164
Ball.R.N., 13
Mislove, M., 1
Banaszczyk, W. 34
Montalvo, F., 101
Brechner, B., 1
Brown, L.M., 40
Burke, D.K., 54 N
agy, Zs., 147
Nikiel,J., 170
^erin, Z., 57
Ciesielski, K., 69
Coplakova, E., ix Pol, R., 175
Purisch, S., 124
Diker, M., 40
Dow, A., 79 R.ajagopalan, M., 124
Font, J.J., 9
Semenov, P.v., 184
Shakhmatov, D., 1
Cjarrido, 1., 101 Sipacheva, O.V., 188
Gianella, G.M., 57 Soukup, L., 147
Szentmiklossy, Z., 147
Hagler, J.N., 13
Mansell, R.W., 54
Titawano, M., i
Hart, K.P., ix
Todd, A.R., 197
Henriksen, M., 108
Hernandez, S., 9
Hota, S., 124
Van Engelen, F., I, 95
Hung, H.H., 133
van Mill, J., ix
Vaughan, J.E., 203
Itzkowitz, G., 138 Vermeer, J., 209
Juhasz, I., 147
AVatson, S., 1
Wong, R.Y., 214
ICovar, M.M., 160 Wu,T.S., 138
z
Larson, S., 108 akrzewski, P., 218
227