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## Main Question or Discussion Point

I need the demostration of the Taimanov's extension theorem:

This theorem said:

Let [tex]A[/tex] be dense in the [tex]T_1[/tex]-space [tex]X[/tex]. Then in order that a continuos function [tex]f[/tex] from [tex]X[/tex] into a compact space [tex]Y[/tex] have a continuous extension [tex]f^*:X\rightarrow Y[/tex] if and only if that for each two disjoint closed sets [tex]F_1[/tex] and [tex]F_2[/tex], [tex]f^{-1}[F_1][/tex] and [tex]f^{-1}[F_2][/tex] have disjoint closures in [tex]X[/tex].

Where can I find the demostration of this theorem?

Thanks

This theorem said:

Let [tex]A[/tex] be dense in the [tex]T_1[/tex]-space [tex]X[/tex]. Then in order that a continuos function [tex]f[/tex] from [tex]X[/tex] into a compact space [tex]Y[/tex] have a continuous extension [tex]f^*:X\rightarrow Y[/tex] if and only if that for each two disjoint closed sets [tex]F_1[/tex] and [tex]F_2[/tex], [tex]f^{-1}[F_1][/tex] and [tex]f^{-1}[F_2][/tex] have disjoint closures in [tex]X[/tex].

Where can I find the demostration of this theorem?

Thanks