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Marius DÄdÄrlat and Terry A. Loring, Deformations of topological spaces predicted by E-theory, In
Algebraic methods in operator theory, p. 316ā327.
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157:. 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
327:
216:". Math 205B-2012 Lecture Notes, University of California Riverside. Retrieved November 16, 2023. See also the accompanying diagram "
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Jean-Marc
Cordier and Tim Porter, (1989), Shape Theory: Categorical Methods of Approximation, Mathematics and its Applications,
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Michael
Batanin, Categorical strong shape theory, Cahiers Topologie GĆ©om. DiffĆ©rentielle CatĆ©g. 38 (1997), no. 1, 3ā66,
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134:) compact spaces, and even onto general categories, by WÅodzimierz HolsztyÅski in year 1968/1969, and published in
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165:, 61ā68, y.1971. Further developments are reflected by the references below, and by their contents.
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106:, just like those of a point, and so any map between the Warsaw circle and a point induces a
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359:, Coherent prohomotopy and strong shape theory, Glasnik MatematiÄki 19(39) (1984) 335ā399.
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141:, 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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335:Äech and Steenrod homotopy theories with applications to geometric topology
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Marius DÄdÄrlat, Shape theory and asymptotic morphisms for C*-algebras,
86:, hence the name of one of the fundamental examples of the area, the
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73:
319:, Theory of Shape, Monografie Matematyczne Tom 59, Warszawa 1975.
233:
90:. It is a compact subset of the plane produced by "closing up" a
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26:
that provides a more global view of the topological spaces than
291:
Mathematical
Proceedings of the Cambridge Philosophical Society
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172:, more sophisticated invariants were developed under the name
352:, 1, 6, 1973, pp. 429ā436; 2, 6, 1973, pp. 667ā675.
289:, Borsuk's shape and Grothendieck categories of pro-objects,
130:
Borsuk's shape theory was generalized onto arbitrary (non-
118:, the Warsaw circle does not have the homotopy type of a
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and Jack Segal, Shapes of compacta and ANR-systems,
214:
The Polish Circle and some of its unusual properties
145:, characteristic for the Äech homology rendered by
42:theory while homotopy theory associates with the
309:, Concerning homotopy properties of compacta,
8:
54:Shape theory was invented and published by
350:Journal of the London Mathematical Society
333:D. A. Edwards and H. M. Hastings, (1976),
324:Äech Theory: its Past, Present, and Future
278:, On the categorical shape of a functor,
205:
328:Rocky Mountain Journal of Mathematics
7:
110:. However these two spaces are not
38:. Shape theory associates with the
330:, Volume 10, Number 3, Summer 1980
322:D. A. Edwards and H. M. Hastings,
218:Constructions on the Polish Circle
34:dominated homotopically by finite
14:
348:Tim Porter, Äech homotopy I, II,
155:Foundations of Algebraic Topology
234:"Thirty years of shape theory"
1:
102:of the Warsaw circle are all
339:Lecture Notes in Mathematics
180:, e.g. the shape theory for
161:and Jack Segal, Fund. Math.
62:in 1968. Actually, the name
245:Mathematical Communications
82:Borsuk lived and worked in
414:
370:Duke Mathematical Journal
108:weak homotopy equivalence
271:. Reprinted Dover (2008)
168:For some purposes, like
311:Fundamenta Mathematicae
301:Fundamenta Mathematicae
280:Fundamenta Mathematicae
178:noncommutative geometry
92:topologist's sine curve
372:, 73(3):687ā711, 1994.
126:Historical development
79:
66:was coined by Borsuk.
30:. The two coincide on
285:Aristide Deleanu and
274:Aristide Deleanu and
176:. Generalizations to
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153:in their monograph
112:homotopy equivalent
98:) with an arc. The
293:79 (1976) 473ā482.
282:97 (1977) 157ā176.
194:List of topologies
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16:Branch of topology
313:62 (1968) 223ā254
287:Peter John Hilton
276:Peter John Hilton
184:have been found.
182:operator algebras
170:dynamical systems
116:Whitehead theorem
96:Warsaw sine curve
78:The Warsaw circle
44:singular homology
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355:J.T. Lisica and
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147:Samuel Eilenberg
143:continuous style
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343:Springer-Verlag
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151:Norman Steenrod
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100:homotopy groups
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307:Karol Borsuk
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174:strong shape
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60:Karol Borsuk
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20:Shape theory
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136:Fund. Math.
387:Categories
377:BirkhƤuser
200:References
120:CW complex
50:Background
36:polyhedra
393:Topology
232:(1997).
188:See also
46:theory.
32:compacta
24:topology
258:at the
251:: 1ā12.
104:trivial
364:numdam
132:metric
84:Warsaw
379:1994.
341:542,
149:and
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