235:
69:. Since the rational numbers are a countable subset of the reals, for example, the irrational numbers are a cocountable subset of the reals. If the complement is finite, then one says
295:
276:
214:
163:
93:, i.e., it is closed under the operations of countable unions, countable intersections, and complementation. This σ-algebra is the
269:
300:
262:
50:
114:
210:
159:
202:
181:
151:
246:
289:
102:
90:
58:
185:
155:
31:
242:
206:
122:
17:
150:, Undergraduate Texts in Mathematics, New York: Springer, pp. 24–30,
74:
234:
38:
146:
Halmos, Paul; Givant, Steven (2009), "Chapter 5: Fields of sets",
197:
James, Ioan
Mackenzie (1999), "Topologies and Uniformities",
117:(also called the "countable complement topology") on any set
250:
180:, "Chapter 29: Boolean σ-algebras", pp. 268–281,
89:that are either countable or cocountable forms a
101:. It is the smallest σ-algebra containing every
270:
8:
177:
65:contains all but countably many elements of
277:
263:
199:Springer Undergraduate Mathematics Series
138:
27:Having all but countably many elements
296:Basic concepts in infinite set theory
7:
231:
229:
25:
233:
148:Introduction to Boolean Algebras
125:and all cocountable subsets of
1:
95:countable-cocountable algebra
249:. You can help Knowledge by
186:10.1007/978-0-387-68436-9_29
156:10.1007/978-0-387-68436-9_5
317:
228:
178:Halmos & Givant (2009)
85:The set of all subsets of
207:10.1007/978-1-4471-3994-2
201:, London: Springer: 33,
245:-related article is a
115:cocountable topology
61:. In other words,
258:
257:
16:(Redirected from
308:
301:Set theory stubs
279:
272:
265:
237:
230:
220:
219:
194:
188:
175:
169:
168:
143:
121:consists of the
21:
316:
315:
311:
310:
309:
307:
306:
305:
286:
285:
284:
283:
226:
224:
223:
217:
196:
195:
191:
176:
172:
166:
145:
144:
140:
135:
111:
83:
28:
23:
22:
15:
12:
11:
5:
314:
312:
304:
303:
298:
288:
287:
282:
281:
274:
267:
259:
256:
255:
238:
222:
221:
215:
189:
170:
164:
137:
136:
134:
131:
110:
107:
82:
79:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
313:
302:
299:
297:
294:
293:
291:
280:
275:
273:
268:
266:
261:
260:
254:
252:
248:
244:
239:
236:
232:
227:
218:
216:9781447139942
212:
208:
204:
200:
193:
190:
187:
183:
179:
174:
171:
167:
165:9780387684369
161:
157:
153:
149:
142:
139:
132:
130:
128:
124:
120:
116:
108:
106:
104:
103:singleton set
100:
96:
92:
88:
80:
78:
76:
72:
68:
64:
60:
59:countable set
56:
52:
48:
44:
40:
37:
33:
19:
251:expanding it
240:
225:
198:
192:
173:
147:
141:
126:
118:
112:
98:
94:
86:
84:
70:
66:
62:
54:
46:
45:is a subset
42:
35:
29:
36:cocountable
32:mathematics
18:Cocountable
290:Categories
243:set theory
133:References
81:σ-algebras
51:complement
123:empty set
91:σ-algebra
41:of a set
109:Topology
75:cofinite
213:
162:
49:whose
39:subset
241:This
57:is a
247:stub
211:ISBN
160:ISBN
113:The
34:, a
203:doi
182:doi
152:doi
97:on
73:is
53:in
30:In
292::
209:,
158:,
129:.
105:.
77:.
278:e
271:t
264:v
253:.
205::
184::
154::
127:X
119:X
99:X
87:X
71:Y
67:X
63:Y
55:X
47:Y
43:X
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.