General TopologySpringer Science & Business Media, 27 Haz 1975 - 298 sayfa Aimed at graduate math students, this classic work is a systematic exposition of general topology and is intended to be a reference and a text. As a reference, it offers a reasonably complete coverage of the area, resulting in a more extended treatment than normally given in a course. As a text, the exposition in the earlier chapters proceeds at a pedestrian pace. A preliminary chapter covers those topics requisite to the main body of work. |
İçindekiler
PRELIMINARIES | 1 |
UNION AND INTERSECTION | 2 |
RELATIONS | 6 |
FUNCTIONS | 10 |
ORDERINGS | 13 |
ALGEBRAIC CONCEPTS | 17 |
THE REAL NUMBERS | 19 |
COUNTABLE SETS | 25 |
QUOTIENT SPACES | 147 |
COMPACTIFICATION | 149 |
LEBESGUPS COHERING LEMMA | 154 |
PARACOMPACTNESS | 156 |
PROBLEMS | 161 |
UNIFORM SPACES | 174 |
UNIFORMITIES AND THE UNIFORM TOPOLOGY | 175 |
UNIFORM CONTINUITY PRODUCT UNIFORMITIES | 180 |
CARDINAL NUMBERS | 27 |
ORDINAL NUMBERS | 29 |
CARTESIAN PRODUCTS | 30 |
HAUSDORFF MAXIMAL PRINCIPLE | 31 |
TOPOLOGICAL SPACES | 37 |
CLOSED SETS | 40 |
CLOSURE | 42 |
BASES AND SUBBASES | 46 |
CONNECTED SETS | 53 |
PROBLEMS | 55 |
MOORESMITH CONVERGENCE | 62 |
SUBNETS AND CLUSTER POINTS | 69 |
SEQUENCES AND SUBSEQUENCES | 72 |
CONVERGENCECLASSES | 73 |
PROBLEMS | 76 |
PRODUCT AND QUOTIENT SPACES | 84 |
PRODUCT SPACES | 88 |
QUOTIENT SPACES | 94 |
PROBLEMS | 100 |
EMBEDDING AND METRIZATION | 111 |
EMBEDDING IN CUBES | 115 |
METRIC AND PSEUDOMETRIC SPACES | 118 |
METRIZATION | 124 |
PROBLEMS | 130 |
COMPACT SPACES | 135 |
PRODUCTS OF COMPACT SPACES | 143 |
LOCALLY COMPACT SPACES | 146 |
METRIZATION | 184 |
COMPLETENESS | 190 |
COMPLETION | 195 |
COMPACT SPACES | 197 |
FOR METRIC SPACES ONLY | 200 |
PROBLEMS | 203 |
FUNCTION SPACES | 217 |
COMPACT OPEN TOPOLOGY AND JOINT CONTINUITY | 221 |
UNIFORM CONVERGENCE | 225 |
UNIFORM CONVERGENCE ON COMPACTA | 229 |
COMPACTNESS AND EQUICONTINUITY | 231 |
EVEN CONTINUITY | 234 |
PROBLEMS | 238 |
ELEMENTARY SET THEORY | 250 |
THE CLASSIFICATION AXIOM SCHEME | 251 |
EXISTENCE OF SETS | 256 |
RELATIONS | 259 |
FUNCTIONS | 260 |
WELL ORDERING | 262 |
ORDINALS | 266 |
INTEGERS | 271 |
THE CHOICE AXIOM | 272 |
CARDINAL NUMBERS | 274 |
| 282 | |
| 293 | |
Diğer baskılar - Tümünü görüntüle
Sık kullanılan terimler ve kelime öbekleri
accumulation point axiom of countability belongs Boolean cardinal number cartesian product Cauchy Cauchy net closed sets closed subset closure cluster point compact set compact space compact subset compactification complement complete Consequently contains continuous functions coordinate space countable base defined definition disjoint domain f equicontinuous equivalent family of sets finite intersection finite number follows function ƒ ƒ is continuous Hausdorff space hence homeomorphic identical jointly continuous lemma Let F linear locally compact locally finite maximal metric space neighborhood system non-void open cover open set open subset ordinal pairs paracompact pointwise convergence product space product topology proposition pseudo-metric pseudo-metric space quotient space quotient topology real numbers real-valued function relative satisfies sequence subbase subcover subfamily subspace summable Suppose THEOREM Let tion topological group topological space Tychonoff space uniform space uniform space X,u uniformly continuous union upper bound usual topology X X X