If pick open sets and (all open in their respective topologies) such that and and . What happens if ?
Let pick such that , and then what about and
Q1:-
If ( X , T) & ( Y , J ) are both Hausdrff space`s , so is ( X x Y , P X x Y ) .
remark:- P X x Y = the topology of the basis of ( X x Y )
Q2:-
A subspace of a Hausdrff space is also a Hausdrff space .
Whith many many thnx
first of all :- many many thnk`s for your help
now
the first section is 100% true
but then ....???
Let pick such that , and then what about and [/QUOTE]
how came Y be a subset of X ??!!!!!
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now i think that , we begin with
let
&
then same how we will get a contradiction ( how i don`t know ) ???