Biblioteca de la Universidad Complutense de Madrid

A topology for the sets of shape morphisms


Cuchillo Ibáñez, Eduardo y Morón, Manuel A. y Romero Ruiz del Portal, Francisco y Rodríguez Sanjurjo, José Manuel (1999) A topology for the sets of shape morphisms. Topology and its Applications, 94 (1-3). pp. 51-60. ISSN 0166-8641

[img] PDF
Restringido a Sólo personal autorizado del repositorio hasta 31 Diciembre 2020.


URL Oficial:


We introduce a topology on the set of shape morphisms between arbitrary topological spaces X, Y, Sh(X, Y). These spaces allow us to extend, in a natural way, some classical concepts to the realm of topological spaces. Several applications are given to obtain relations between shape theory and N-compactness and shape-theoretic properties of the spaces of quasicomponents.

Tipo de documento:Artículo
Palabras clave:Maps; shape morphism; HPol-expansion; N-compactness; space of quasicomponents
Materias:Ciencias > Matemáticas > Topología
Código ID:15462

B.J. Ball, Shapes of saturated subsets of compacta, Colloq. Math. 29 (1974) 241–246.

B.J. Ball, Quasicompactifications and shape theory, Pacific J. Math. 84 (1979) 251–259.

B.J. Ball, Partitioning shape-equivalent spaces, Bull. Acad. Pol. Math. 29 (1981) 491–497.

S.A. Bogatyĭ, Approximative and fundamental retracts, Mat. Sb. 93 (135) (1974) 90–102.

K. Borsuk, Theory of Shape, Monografie Matematyczne 59 (PWN, Warsaw, 1975).

J. Dydak and M.A. Morón, Quasicomponents and shape theory, Topology Proc. 13 (1988) 73–82.

J. Dydak and J. Segal, Shape Theory: An Introduction, Lecture Notes in Math. 688 (Springer, Berlin, 1978).

K. Eda, T. Kiyosawa and H. Ohta, N-compactness and its applications in: K. Morita and J. Nagata, eds., Topics in General Topology (North-Holland, Amsterdam, 1989) 459–521.

R. Engelking, General Topology, Monografie Matematyczne 60 (PWN, Warsaw, 1977).

R. Engelking and S. Mröwka, On E-compact spaces, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astron. Phys. 6 (1958) 429–436.

L. Gillman and M. Jerison, Rings of Continuous Functions (Springer, Berlin, 1960).

S. Mardešić, Approximate polyhedra resolutions of maps and shape fibrations, Fund. Math. 114 (1981) 53–78.

S. Mardešić and J. Segal, Shape Theory (North-Holland, Amsterdam, 1982).

M.A. Morón, On internal movability; internal shape and internal MANR-spaces, Colloq. Math. 57 (2) (1989) 235–246.

M.A. Morón, N-compactness and shape, Proc. Amer. Math. Soc. 113 (1991) 545–550.

M.A. Morón and F.R. Ruiz del Portal, Ultrametrics and infinite dimensional Whitehead theorems in shape theory, Manuscripta Math. 89 (1996) 325–333.

M.A. Morón and F.R. Ruiz del Portal, Shape as a Cantor completion process, Math. Z. 225 (1997) 67–86.

M.A. Morón and F.R. Ruiz del Portal, Spaces of discrete shape and C-refinable maps that induce shape equivalences, J. Math. Soc. Japan 49 (1997) 713–721.

M.A. Morón, F.R. Ruiz del Portal and J.M.R. Sanjurjo, Shape invariance of N-compactifications, Topology Appl. 56 (1994) 63–71.

P. Nyikos, Prabir Roy’s space Δ is not N-compact, Gen. Topology Appl. 3 (1973) 197–210.

J.M.R. Sanjurjo, On a theorem of B.J. Ball, Bull. Acad. Polon. Sci. 33 (1985) 177–180.

Depositado:01 Jun 2012 10:35
Última Modificación:06 Feb 2014 10:25

Sólo personal del repositorio: página de control del artículo