What is the theory of shape?

DOI10.1017/S000497270000647XzbMath0452.54010MaRDI QIDQ3899156

Jerzy Dydak, Karol Borsuk

Publication date: 1980

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

bibliographymovabilityfundamental dimensioncell-like mapsshape invariantsaddition and multiplication of shapesshape embedding propertiesshape-regular compactashapes of compact metric spacesshapes of topological spaces

Mathematics Subject Classification ID

Shape theory in general topology (54C56) Shape theory (55P55) Research exposition (monographs, survey articles) pertaining to general topology (54-02) Research exposition (monographs, survey articles) pertaining to algebraic topology (55-02) Shapes (aspects of topological manifolds) (57N25) Shape groups (55Q07)

Related Items (8)

A comprehensive study of clustering a class of 2D shapes ⋮ Homotopy decompositions of polyhedra into products with the second factor \(S^1\) ⋮ Cartesian powers of shapes of FANR's and polyhedra ⋮ On weakly continuum-chainable and almost continuum-chainable continua ⋮ A connected 4-dimensional polyhedron with two homotopy decompositions into prime factors ⋮ On some problem of Borsuk concerning decompositions of shapes into prime factors ⋮ A continuum with no prime shape factors ⋮ Shape theory

Cites Work

• Unnamed Item
• Unnamed Item
• Characterizations of tree-like continua
• Mapping Hilbert cube manifolds to ANR's: A solution of a conjecture of Borsuk
• On the shape of decomposition spaces
• Shapes of complexes, ends of manifolds, homotopy limits and the Wall obstruction
• Etale homotopy
• Approximating cellular maps by homeomorphisms
• Some theorems on absolute neighborhood retracts
• Shape Theory and Compact Connected Abelian Topological Groups
• A counterexample in shape theory
• The Stability Problem in Shape, and a Whitehead Theorem in Pro-Homotopy
• Infinite-Dimensional Whitehead and Vietoris Theorems in Shape and Pro-Homotopy
• An Algebraic Property of the Cech Cohomology Groups Which Prevents Local Connectivity and Movability
• Cell-like mappings and their generalizations
• Simple homotopy theory for ANR's
• Shape fibrations I
• Elementary proofs of stability theorems in pro-homotopy and shape
• Concerning the Shapes of Finite-Dimensional Compacta
• Property SUV ∞ and Proper Shape Theory
• An Example in Cech Cohomology
• Cellular decompositions of 3-manifolds that yield 3-manifolds
• Realizing cell-like maps in Euclidean space
• Compact Hilbert cube manifolds and the invariance of Whitehead torsion
• Shapes for topological spaces
• On the Shape of Torus-Like Continua and Compact Connected Topological Groups
• Simplicial Spaces, Nuclei and m -Groups
• On the homotopy type of ANR’s

This page was built for publication: What is the theory of shape?