Brown–Booth–Tillotson theory for classes of exponentiable spaces

Brown, Booth and Tillotson introduced the C -product, or the BBT C -product, for any class C of topological spaces. It is proved that any topological space is exponentiable with respect to the BBT C -product if and only if C is a subclass of the class of exponentiable spaces. The topology of the fun...

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Bibliographic Details
Published in:Topology and its Applications Vol. 156; no. 13; pp. 2264 - 2283
Main Authors: Hirashima, Yasumasa, Oda, Nobuyuki
Format: Journal Article
Language:English
Japanese
Published: Elsevier B.V 01.08.2009
Elsevier BV
Subjects:
Compact-open
Function space
Geometry and Topology
Homotopy
k-space
Test-open
k-space
Function space
Compact-open
Test-open
Homotopy
ISSN:0166-8641, 1879-3207
Online Access:Get full text
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Summary:Brown, Booth and Tillotson introduced the C -product, or the BBT C -product, for any class C of topological spaces. It is proved that any topological space is exponentiable with respect to the BBT C -product if and only if C is a subclass of the class of exponentiable spaces. The topology of the function space is induced by a canonical manner making use of the exponential topology for the spaces in C . It is not the C -open topology in general. The function space defined by this method enjoys good properties for algebraic topology. A necessary and sufficient condition on the class C is obtained for the exponential function to be a homeomorphism with the BBT C -product.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2009.05.012