On shape of hyperspaces
Y. Kodama, S. Spież, T. Watanabe (1978)
Fundamenta Mathematicae
Kiiti Morita (1975)
Fundamenta Mathematicae
Fujitsugu Hosokawa, Shin'ichi Suzuki (1995)
Revista Matemática de la Universidad Complutense de Madrid
In the study of surfaces in 3-manifolds, the so-called ?cut-and-paste? of surfaces is frequently used. In this paper, we generalize this method, in a sense, to singular-surfaces, and as an application, we prove that two collections of singular-disks in the 3-space R3 which span the same trivial link are link-homotopic in the upper-half 4-space R3 [0,8) keeping the link fixed. Throughout the paper, we work in the piecewise linear category, consisting of simplicial complexes and piecewise linear maps....
T. Chapman (1972)
Fundamenta Mathematicae
I. Pop (1996)
Revista Matemática de la Universidad Complutense de Madrid
Related to Shape Theory, in a previous paper (1992) we studied weak monomorphisms and weak epimorphisms in the category of pro-groups. In this note we give some intrinsic characterizations of the weak monomorphisms and the weak epimorphisms in pro-HTop* in the case when one of the two objects of such a morphism is a rudimentary system.
Félix, Yves, Thomas, Jean-Claude (1999)
Homology, Homotopy and Applications
Luc Demers (1975)
Fundamenta Mathematicae
Hans-Joachim Baues, Daniel Conduché (1997)
Forum mathematicum
Baker, Andrew, Lazarev, Andrej (2001)
Algebraic & Geometric Topology
Marco Grandis (1992)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
Aristide Delenau, Peter Hilton (1977)
Fundamenta Mathematicae
Cordovil, Raul (1994)
Portugaliae Mathematica
P.J. Hilton, J. Roitberg (1970)
Commentarii mathematici Helvetici
Menichi, Luc (2001)
Algebraic & Geometric Topology
Michael Slack (1992)
Mathematische Zeitschrift
Mohammad Parhizgar (1997)
Mathematica Scandinavica
Imre Bokor (1990)
Publicacions Matemàtiques
The Hilton-Hopf quadratic form is defined for spaces of the homotopy type of a CW complex with one cell each in dimensions 0 and 4n, K cells in dimension 2n and no other cells. If two such spaces are of the same topological genus, then their Hilton-Hopf quadratic forms are of the same weak algebraic genus. For large classes of spaces, such as simply connected differentiable 4-manifolds, the converse is also true, as long as the suspensions of the spaces are also of the same topological genus. This...
Jacob Mostovoy, Rustam Sadykov (2012)
Fundamenta Mathematicae
We prove that the space of nonempty subsets of cardinality at most k in a bouquet of m+1-dimensional spheres is (m+k-2)-connected. This, as shown by Tuffley, implies that the space is (m+k-2)-connected for any m-connected cell complex X.
J. Eells, L. Lemaire (1980)
Mathematische Annalen
A. Zabrodsky (1972)
Inventiones mathematicae