- #1
conquest
- 133
- 4
Hi all!
My question is the following. Suppose we have two normal topological spaces X and Y and we have a continuous map from a closed subset A of X to Y. Then we can construct another topological space by "glueing together" X and Y at A and f(A). By taking the quotient space of the disjoint union of X and Y by the equivalence relation that
x is equivalent to y if:
1) x=y
2) x,y are elements of A and f(x)=f(y)
or
3) x is an element of A and y is an element of Y and f(x)=y
or x is an element of Y and y is an element of A and x=f(y).
My question is how can you prove that this constructed space is again normal?
My question is the following. Suppose we have two normal topological spaces X and Y and we have a continuous map from a closed subset A of X to Y. Then we can construct another topological space by "glueing together" X and Y at A and f(A). By taking the quotient space of the disjoint union of X and Y by the equivalence relation that
x is equivalent to y if:
1) x=y
2) x,y are elements of A and f(x)=f(y)
or
3) x is an element of A and y is an element of Y and f(x)=y
or x is an element of Y and y is an element of A and x=f(y).
My question is how can you prove that this constructed space is again normal?