561:
205:
678:, (2006) available from amazon sites. Discusses the homotopy type of adjunction spaces, and uses adjunction spaces as an introduction to (finite) cell complexes.
684:"Note on a theorem due to Borsuk" Bull AMS 54 (1948), 1125-1132 is the earliest outside reference I know of using the term "adjuction space".
544:
671:
702:
151:
630:
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are the maps obtained by composing the quotient map with the canonical injections into the disjoint union of
315:. Inductively attaching cells along their spherical boundaries to this space results in an example of a
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before attaching the boundaries of the removed balls along an attaching map.
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263:). The topology, however, is specified by the quotient construction.
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651:, (1970) Addison-Wesley Publishing Company, Reading Massachusetts.
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is also an inclusion the attaching construction is to simply glue
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is a space with one point then the adjunction is the quotient
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are in 1-1 correspondence with the pairs of continuous maps
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is attached or "glued" onto another. Specifically, let
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A common example of an adjunction space is given when
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is a space with one point then the adjunction is the
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609:—the construction is similar. Conversely, if
601:. One can form a more general pushout by replacing
199:
539:The attaching construction is an example of a
200:{\displaystyle X\cup _{f}Y=(X\sqcup Y)/\sim }
8:
547:. That is to say, the adjunction space is
330:. Here, one first removes open balls from
322:Adjunction spaces are also used to define
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153:
676:"Topology and Groupoids" pdf available
621:together along their common subspace.
653:(Provides a very brief introduction.)
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307:is the boundary of the ball, the (
251:consists of the disjoint union of
87:). One forms the adjunction space
25:
605:with an arbitrary continuous map
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234:, and the quotient is given the
55:be topological spaces, and let
551:with respect to the following
545:category of topological spaces
266:Intuitively, one may think of
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39:) is a common construction in
1:
100:(sometimes also written as
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489:one can show that the map
535:Categorical description
531:is an open embedding.
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381:The continuous maps
270:as being glued onto
212:equivalence relation
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553:commutative diagram
703:Topological spaces
659:"Adjunction space"
477:In the case where
214:~ is generated by
197:
647:Stephen Willard,
236:quotient topology
45:topological space
16:(Redirected from
710:
682:J.H.C. Whitehead
668:
649:General Topology
636:Mapping cylinder
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125:and identifying
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33:adjunction space
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18:Attaching map
672:Ronald Brown
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485:subspace of
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291:is a closed
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238:. As a set,
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145:. Formally,
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83:(called the
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36:
32:
26:
29:mathematics
692:Categories
664:PlanetMath
642:References
466:) for all
377:Properties
317:CW complex
226:) for all
210:where the
137:) for all
43:where one
549:universal
508:embedding
347:wedge sum
328:manifolds
195:∼
181:⊔
160:∪
698:Topology
625:See also
432:→
428: :
415:→
411: :
398:→
385: :
282:Examples
71: :
61:subspace
41:topology
571:is the
543:in the
541:pushout
483:closed
313:sphere
303:) and
67:. Let
567:Here
510:and (
481:is a
255:and (
129:with
79:be a
59:be a
31:, an
617:and
597:and
575:and
518:) →
419:and
353:and
334:and
311:−1)-
301:cell
299:(or
297:ball
121:and
51:and
35:(or
470:in
453:))=
360:If
349:of
341:If
326:of
230:in
141:in
117:of
63:of
27:In
694::
674:,
661:.
584:,
555::
514:−
493:→
474:.
278:.
259:−
218:~
75:→
667:.
619:Y
615:X
611:f
607:g
603:i
599:Y
595:X
590:Y
586:Φ
581:X
577:Φ
569:i
529:Y
525:f
522:∪
520:X
516:A
512:Y
504:Y
500:f
497:∪
495:X
491:X
487:Y
479:A
472:A
468:a
464:a
462:(
459:Y
455:h
451:a
449:(
447:f
445:(
442:X
438:h
434:Z
430:Y
425:Y
421:h
417:Z
413:X
408:X
404:h
400:Z
396:Y
392:f
389:∪
387:X
383:h
372:.
370:A
368:/
366:Y
362:X
357:.
355:Y
351:X
343:A
336:Y
332:X
319:.
309:n
305:A
295:-
293:n
289:Y
276:f
272:X
268:Y
261:A
257:Y
253:X
249:Y
245:f
242:∪
240:X
232:A
228:a
224:a
222:(
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191:/
187:)
184:Y
178:X
175:(
172:=
169:Y
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135:a
133:(
131:f
127:a
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119:X
111:Y
107:f
104:+
102:X
98:Y
94:f
91:∪
89:X
77:X
73:A
69:f
65:Y
57:A
53:Y
49:X
20:)
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