Let (X, T) and (Y, T₁) be two topological spaces and let f be a continuous mapping of X into Y. O If f is onto and (Y,T_1) is a T_1 space then (X,T) is a T_1 space. O If f is one-to-one and (Y,T_1 ) is a T_1 space then (X,T) is a T_1 space. O None of the choices. O If (Y,T_1) is a Hausdorff space then (X,T) is a Hausdorff space.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Let (X, T) and (Y, T₁) be two topological spaces and let f be a continuous mapping of X into Y.
If f is onto and (Y,T_1) is a T_1 space then
(X,T) is a T_1 space.
If f is one-to-one and (Y,T_1 ) is a T_1 space
then (X,T) is a T_1 space.
None of the choices.
If (Y,T_1) is a Hausdorff space then (X,T) is
a Hausdorff space.
Transcribed Image Text:Let (X, T) and (Y, T₁) be two topological spaces and let f be a continuous mapping of X into Y. If f is onto and (Y,T_1) is a T_1 space then (X,T) is a T_1 space. If f is one-to-one and (Y,T_1 ) is a T_1 space then (X,T) is a T_1 space. None of the choices. If (Y,T_1) is a Hausdorff space then (X,T) is a Hausdorff space.
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