Main Article Content
<i>C<sub>b</sub>(X)</i> Revisited: Induced map and Submetrizability
Abstract
This paper, in the first half, studies the induced map on the
space Cb(X) of all continuous
real-valued functions on a Tychonoff space X, where
the function space has the bounded-open topology. In the second half, the submetrizability
of Cb(X) is studied in
detail.
Mathematics Subject Classification (2000): 54C35, 54C10, 54E18, 54E99.
Key words: Function space, induced map, μ-space, quasi-μ-space, submetrizability, pseudocompact, Cech-complete.
Quaestiones Mathematicae 27 (2004), 47-56.
space Cb(X) of all continuous
real-valued functions on a Tychonoff space X, where
the function space has the bounded-open topology. In the second half, the submetrizability
of Cb(X) is studied in
detail.
Mathematics Subject Classification (2000): 54C35, 54C10, 54E18, 54E99.
Key words: Function space, induced map, μ-space, quasi-μ-space, submetrizability, pseudocompact, Cech-complete.
Quaestiones Mathematicae 27 (2004), 47-56.
