272:
121:
106:
313:
337:
342:
306:
114:
332:
299:
287:
29:
220:
Remmert, Reinhold; Stein, Karl (1953), "Über die wesentlichen
Singularitäten analytischer Mengen",
97:
is analytic in the complex plane minus the origin, but its closure in the complex plane is not.
279:
222:
251:
8:
255:
208:
147:
37:
259:
239:
212:
231:
198:
172:
56:
41:
25:
17:
247:
89:
The condition on the dimensions is necessary: for example, the set of points (1/
283:
110:
326:
243:
177:
160:
105:
A consequence of the
Remmert–Stein theorem (also treated in their paper), is
94:
203:
186:
235:
152:
271:
163:(1964), "Conditions for the Analycity of certain sets",
142:
Aguilar, Carlos Martínez; Verjovsky, Alberto (2021),
324:
141:
129:
100:
307:
219:
191:Journal of the Mathematical Society of Japan
33:
187:"Sur le théorème de P. Thullen et K. Stein"
314:
300:
120:The Remmert–Stein theorem is implied by a
74:with all components of dimension at least
51:is an analytic set of dimension less than
202:
176:
151:
325:
159:
125:
266:
184:
109:stating that any projective complex
13:
14:
354:
270:
82:is either analytic or contains
130:Aguilar & Verjovsky (2021)
20:, a field in mathematics, the
1:
135:
338:Theorems in complex analysis
286:. You can help Knowledge by
115:projective algebraic variety
36:), gives conditions for the
7:
343:Mathematical analysis stubs
101:Relations to other theorems
47:The theorem states that if
10:
359:
265:
66:is an analytic subset of
144:Chow's Theorem Revisited
282:–related article is a
178:10.1307/mmj/1028999180
122:proper mapping theorem
78:, then the closure of
280:mathematical analysis
223:Mathematische Annalen
204:10.2969/jmsj/01820211
185:Kato, Kazuko (1966).
22:Remmert–Stein theorem
26:Reinhold Remmert
236:10.1007/BF01343164
333:Complex manifolds
295:
294:
165:Michigan Math. J.
113:is necessarily a
350:
316:
309:
302:
274:
267:
262:
216:
206:
181:
180:
156:
155:
57:complex manifold
44:to be analytic.
24:, introduced by
18:complex analysis
358:
357:
353:
352:
351:
349:
348:
347:
323:
322:
321:
320:
138:
103:
12:
11:
5:
356:
346:
345:
340:
335:
319:
318:
311:
304:
296:
293:
292:
275:
264:
263:
217:
182:
171:(4): 289–304,
161:Bishop, Errett
157:
137:
134:
111:analytic space
107:Chow's theorem
102:
99:
9:
6:
4:
3:
2:
355:
344:
341:
339:
336:
334:
331:
330:
328:
317:
312:
310:
305:
303:
298:
297:
291:
289:
285:
281:
276:
273:
269:
268:
261:
257:
253:
249:
245:
241:
237:
233:
229:
225:
224:
218:
214:
210:
205:
200:
196:
192:
188:
183:
179:
174:
170:
166:
162:
158:
154:
149:
145:
140:
139:
133:
131:
127:
126:Bishop (1964)
123:
118:
116:
112:
108:
98:
96:
95:complex plane
92:
87:
85:
81:
77:
73:
70: –
69:
65:
61:
58:
54:
50:
45:
43:
39:
35:
31:
28: and
27:
23:
19:
288:expanding it
277:
227:
221:
194:
190:
168:
164:
143:
119:
104:
90:
88:
83:
79:
75:
71:
67:
63:
59:
52:
48:
46:
42:analytic set
21:
15:
230:: 263–306,
93:,0) in the
327:Categories
153:2101.09872
136:References
30:Karl Stein
260:119966389
244:0025-5831
213:122821030
55:in some
252:0060033
124:due to
38:closure
32: (
258:
250:
242:
211:
128:, see
62:, and
40:of an
278:This
256:S2CID
209:S2CID
197:(2).
148:arXiv
284:stub
240:ISSN
34:1953
232:doi
228:126
199:doi
173:doi
16:In
329::
254:,
248:MR
246:,
238:,
226:,
207:.
195:18
193:.
189:.
169:11
167:,
146:,
132:.
117:.
86:.
315:e
308:t
301:v
290:.
234::
215:.
201::
175::
150::
91:n
84:F
80:M
76:k
72:F
68:D
64:M
60:D
53:k
49:F
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.