86:
301:
334:
386:
Marius DÄdÄrlat and Terry A. Loring, Deformations of topological spaces predicted by E-theory, In
Algebraic methods in operator theory, p. 316ā327.
345:
66:
168:. Due to the circumstance, HolsztyÅski's paper was hardly noticed, and instead a great popularity in the field was gained by a later paper by
227:". Math 205B-2012 Lecture Notes, University of California Riverside. Retrieved November 16, 2023. See also the accompanying diagram "
278:
Jean-Marc
Cordier and Tim Porter, (1989), Shape Theory: Categorical Methods of Approximation, Mathematics and its Applications,
338:
373:
Michael
Batanin, Categorical strong shape theory, Cahiers Topologie GĆ©om. DiffĆ©rentielle CatĆ©g. 38 (1997), no. 1, 3ā66,
353:
145:) compact spaces, and even onto general categories, by WÅodzimierz HolsztyÅski in year 1968/1969, and published in
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176:, 61ā68, y.1971. Further developments are reflected by the references below, and by their contents.
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117:, just like those of a point, and so any map between the Warsaw circle and a point induces a
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122:
370:, Coherent prohomotopy and strong shape theory, Glasnik MatematiÄki 19(39) (1984) 335ā399.
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152:, 157ā168, y. 1971 (see Jean-Marc Cordier, Tim Porter, (1989) below). This was done in a
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in 1944; it was reinvented, further developed and promoted by the Polish mathematician
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346:Äech and Steenrod homotopy theories with applications to geometric topology
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42:
379:
Marius DÄdÄrlat, Shape theory and asymptotic morphisms for C*-algebras,
130:
97:, hence the name of one of the fundamental examples of the area, the
34:
330:, Theory of Shape, Monografie Matematyczne Tom 59, Warszawa 1975.
244:
101:. It is a compact subset of the plane produced by "closing up" a
85:
37:
that provides a more global view of the topological spaces than
302:
Mathematical
Proceedings of the Cambridge Philosophical Society
94:
183:, more sophisticated invariants were developed under the name
363:, 1, 6, 1973, pp. 429ā436; 2, 6, 1973, pp. 667ā675.
300:, Borsuk's shape and Grothendieck categories of pro-objects,
270:
141:
Borsuk's shape theory was generalized onto arbitrary (non-
249:
129:, the Warsaw circle does not have the homotopy type of a
310:
and Jack Segal, Shapes of compacta and ANR-systems,
225:
The Polish Circle and some of its unusual properties
156:, characteristic for the Äech homology rendered by
53:theory while homotopy theory associates with the
395:
320:, Concerning homotopy properties of compacta,
65:Shape theory was invented and published by
361:Journal of the London Mathematical Society
344:D. A. Edwards and H. M. Hastings, (1976),
335:Äech Theory: its Past, Present, and Future
289:, On the categorical shape of a functor,
136:
239:
84:
14:
396:
339:Rocky Mountain Journal of Mathematics
121:. However these two spaces are not
49:. Shape theory associates with the
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341:, Volume 10, Number 3, Summer 1980
333:D. A. Edwards and H. M. Hastings,
229:Constructions on the Polish Circle
45:dominated homotopically by finite
25:
420:
359:Tim Porter, Äech homotopy I, II,
166:Foundations of Algebraic Topology
80:
245:"Thirty years of shape theory"
217:
13:
1:
210:
113:of the Warsaw circle are all
60:
350:Lecture Notes in Mathematics
191:, e.g. the shape theory for
172:and Jack Segal, Fund. Math.
73:in 1968. Actually, the name
7:
256:Mathematical Communications
198:
93:Borsuk lived and worked in
10:
425:
381:Duke Mathematical Journal
119:weak homotopy equivalence
282:. Reprinted Dover (2008)
179:For some purposes, like
322:Fundamenta Mathematicae
312:Fundamenta Mathematicae
291:Fundamenta Mathematicae
189:noncommutative geometry
103:topologist's sine curve
383:, 73(3):687ā711, 1994.
137:Historical development
90:
77:was coined by Borsuk.
41:. The two coincide on
296:Aristide Deleanu and
285:Aristide Deleanu and
187:. Generalizations to
88:
164:in their monograph
123:homotopy equivalent
109:) with an arc. The
304:79 (1976) 473ā482.
293:97 (1977) 157ā176.
205:List of topologies
91:
27:Branch of topology
324:62 (1968) 223ā254
298:Peter John Hilton
287:Peter John Hilton
195:have been found.
193:operator algebras
181:dynamical systems
127:Whitehead theorem
107:Warsaw sine curve
89:The Warsaw circle
55:singular homology
16:(Redirected from
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366:J.T. Lisica and
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158:Samuel Eilenberg
154:continuous style
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409:Homotopy theory
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354:Springer-Verlag
314:72 (1971) 41ā59
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162:Norman Steenrod
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111:homotopy groups
105:(also called a
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125:. So by the
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71:Karol Borsuk
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147:Fund. Math.
398:Categories
388:BirkhƤuser
211:References
131:CW complex
61:Background
47:polyhedra
404:Topology
243:(1997).
199:See also
57:theory.
43:compacta
35:topology
269:at the
262:: 1ā12.
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375:numdam
143:metric
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390:1994.
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