Cuchillo Ibáñez, Eduardo and Morón, Manuel A. and Romero Ruiz del Portal, Francisco and 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
Restricted to Repository staff only until 31 December 2020.
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.
|Uncontrolled Keywords:||Maps; shape morphism; HPol-expansion; N-compactness; space of quasicomponents|
|Subjects:||Sciences > Mathematics > Topology|
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.
|Deposited On:||01 Jun 2012 12:35|
|Last Modified:||31 Oct 2013 18:45|