166:, which ostensively claims to characterise locally bounded maps among linear maps between (topological) vector spaces. The claims would only hold with respect to sufficiently compatible bornologies on the vector spaces, but neither vector bornologies nor even the canonical / von Neumann bornology of a TVS have been discussed earlier in the article. The removed material (inculded below this comment) could be modified to fit a further expanded discussions of vector bornologies later in the article, but in its original location it was quite misleading and/or incomprehensible to people not knowledgeable of the topic.
84:
74:
53:
22:
174:
appearing without qualification with two meanings, referring on the one hand to members of a given bornology on a set (or a vector space space) and on the other hand to the (von
Neumann) bounded sets of topological vectors spaces, which form a particular (if very common) bornology on a TVS.
169:
In addition, the short section on bornologies on a topological vector spaces comes late and is (considering also the history of the subject) very short and limited. Further confusion is likely to arise from the terminology
140:
377:
263:
570:
339:
547:
527:
500:
476:
448:
421:
401:
316:
286:
227:
207:
603:
130:
598:
503:
424:
106:
97:
58:
33:
230:
21:
451:
296:
39:
83:
105:
on
Knowledge. If you would like to participate, please visit the project page, where you can join
89:
73:
52:
343:
236:
580:
479:
292:
552:
321:
532:
512:
485:
461:
433:
406:
386:
301:
271:
212:
192:
592:
576:
102:
79:
529:
maps null sequences (that is, sequences converging to the origin
584:
265:
is a linear map. Then the following statements are equivalent:
15:
555:
535:
515:
488:
464:
436:
409:
389:
346:
324:
304:
274:
239:
215:
195:
101:, a collaborative effort to improve the coverage of
564:
541:
521:
494:
470:
442:
415:
395:
371:
333:
310:
280:
257:
221:
201:
158:Removed subsection; consistence and clarity issues
295:(that is, bounded in the bornological sense)
8:
506:then this list may be extended to include:
427:then this list may be extended to include:
19:
162:I removed from the article the subsection
47:
554:
534:
514:
487:
463:
435:
408:
388:
351:
345:
323:
303:
273:
238:
214:
194:
49:
7:
95:This article is within the scope of
38:It is of interest to the following
14:
604:Low-priority mathematics articles
115:Knowledge:WikiProject Mathematics
599:Start-Class mathematics articles
118:Template:WikiProject Mathematics
82:
72:
51:
20:
135:This article has been rated as
366:
360:
249:
1:
109:and see a list of open tasks.
288:is a (locally) bounded map;
620:
549:) into bounded subsets of
585:16:58, 1 April 2024 (UTC)
372:{\displaystyle f^{-1}(D)}
231:topological vector spaces
134:
67:
46:
258:{\displaystyle f:X\to Y}
141:project's priority scale
508:
429:
98:WikiProject Mathematics
566:
543:
523:
496:
472:
444:
417:
397:
373:
335:
312:
282:
259:
223:
203:
28:This article is rated
567:
544:
524:
497:
473:
445:
418:
398:
374:
336:
313:
283:
260:
224:
204:
553:
533:
513:
486:
462:
434:
407:
387:
379:is also bornivorous.
344:
322:
302:
272:
237:
213:
193:
121:mathematics articles
565:{\displaystyle Y.}
562:
539:
519:
492:
468:
440:
413:
393:
369:
334:{\displaystyle Y,}
331:
308:
278:
255:
219:
199:
90:Mathematics portal
34:content assessment
542:{\displaystyle 0}
522:{\displaystyle f}
495:{\displaystyle Y}
471:{\displaystyle X}
454:to bounded disks;
443:{\displaystyle f}
416:{\displaystyle Y}
396:{\displaystyle X}
311:{\displaystyle D}
281:{\displaystyle f}
222:{\displaystyle Y}
202:{\displaystyle X}
185:Characterizations
180:Removed material:
164:Characterizations
155:
154:
151:
150:
147:
146:
611:
571:
569:
568:
563:
548:
546:
545:
540:
528:
526:
525:
520:
501:
499:
498:
493:
480:seminormed space
477:
475:
474:
469:
449:
447:
446:
441:
422:
420:
419:
414:
402:
400:
399:
394:
378:
376:
375:
370:
359:
358:
340:
338:
337:
332:
317:
315:
314:
309:
287:
285:
284:
279:
264:
262:
261:
256:
228:
226:
225:
220:
208:
206:
205:
200:
123:
122:
119:
116:
113:
92:
87:
86:
76:
69:
68:
63:
55:
48:
31:
25:
24:
16:
619:
618:
614:
613:
612:
610:
609:
608:
589:
588:
551:
550:
531:
530:
511:
510:
484:
483:
460:
459:
432:
431:
405:
404:
385:
384:
347:
342:
341:
320:
319:
300:
299:
270:
269:
235:
234:
211:
210:
191:
190:
187:
160:
120:
117:
114:
111:
110:
88:
81:
61:
32:on Knowledge's
29:
12:
11:
5:
617:
615:
607:
606:
601:
591:
590:
574:
573:
572:
561:
558:
538:
518:
504:locally convex
491:
467:
456:
455:
450:takes bounded
439:
425:locally convex
412:
392:
381:
380:
368:
365:
362:
357:
354:
350:
330:
327:
307:
289:
277:
254:
251:
248:
245:
242:
218:
198:
186:
183:
177:
159:
156:
153:
152:
149:
148:
145:
144:
133:
127:
126:
124:
107:the discussion
94:
93:
77:
65:
64:
56:
44:
43:
37:
26:
13:
10:
9:
6:
4:
3:
2:
616:
605:
602:
600:
597:
596:
594:
587:
586:
582:
578:
559:
556:
536:
516:
509:
507:
505:
489:
481:
465:
453:
437:
430:
428:
426:
410:
390:
363:
355:
352:
348:
328:
325:
305:
298:
294:
290:
275:
268:
267:
266:
252:
246:
243:
240:
232:
216:
196:
189:Suppose that
184:
182:
181:
176:
173:
167:
165:
157:
142:
138:
132:
129:
128:
125:
108:
104:
100:
99:
91:
85:
80:
78:
75:
71:
70:
66:
60:
57:
54:
50:
45:
41:
35:
27:
23:
18:
17:
575:
457:
382:
188:
179:
178:
172:bounded sets
171:
168:
163:
161:
137:Low-priority
136:
96:
62:Low‑priority
40:WikiProjects
293:bornivorous
233:(TVSs) and
112:Mathematics
103:mathematics
59:Mathematics
30:Start-class
593:Categories
291:For every
139:on the
577:Stca74
36:scale.
478:is a
452:disks
581:talk
482:and
423:are
403:and
297:disk
229:are
209:and
502:is
458:If
383:If
318:in
131:Low
595::
583:)
353:−
250:→
579:(
560:.
557:Y
537:0
517:f
490:Y
466:X
438:f
411:Y
391:X
367:)
364:D
361:(
356:1
349:f
329:,
326:Y
306:D
276:f
253:Y
247:X
244::
241:f
217:Y
197:X
143:.
42::
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
