Re: Topology with base and ...

On 30-10-2007 17:10, mina_world wrote:

Let f : (X, T) -> (Y, T') be open and onto,

and let P be a base for T.

Then P' = {f[B] | B in P} is a base for T'.

This is not true. Let (Y,T') be any topological space with more
that two open sets, take X = Y and take T = {empty set,X}. Then
T is a topology on X, the identity map is open and onto, {X} is a
base for T, but {f(B) | B in P} = {Y}, which is not a base for T'.

Best regards,

Jose Carlos Santos
.

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