- Thread starter
- #1
- Mar 10, 2012
- 834
On pg 70 in Armstrong's Basic Topology book, the author writes:
" We introduce the disjoint union $X+Y$ of spaces $X,Y,$ and the function $j:X+Y \rightarrow X \cup Y$ which when restricted to either $X$ or $Y$ is just the inclusion in $X \cup Y$. This function is important for our purposes because:
a) it is continuous
b) the composition $(f \cup g)j: X+Y \rightarrow Z$ is continuous if and only if both $f$ and $g$ are continuous. "
The author does not mention anything about disjoint union before this. I also checked the index at the back of the book and did not find it. I found one definition of disjoint union on wiki. If I go by that definition then $X$ is not even a subset of $X+Y$ so I don't know what the author is trying to say when he writes '... the function $j:X+Y \rightarrow X \cup Y$ which when restricted to either $X$ or $Y$ ...'
Does anybody have a clue what is the meaning of disjoint union intended here and what this function $j$ might be?
" We introduce the disjoint union $X+Y$ of spaces $X,Y,$ and the function $j:X+Y \rightarrow X \cup Y$ which when restricted to either $X$ or $Y$ is just the inclusion in $X \cup Y$. This function is important for our purposes because:
a) it is continuous
b) the composition $(f \cup g)j: X+Y \rightarrow Z$ is continuous if and only if both $f$ and $g$ are continuous. "
The author does not mention anything about disjoint union before this. I also checked the index at the back of the book and did not find it. I found one definition of disjoint union on wiki. If I go by that definition then $X$ is not even a subset of $X+Y$ so I don't know what the author is trying to say when he writes '... the function $j:X+Y \rightarrow X \cup Y$ which when restricted to either $X$ or $Y$ ...'
Does anybody have a clue what is the meaning of disjoint union intended here and what this function $j$ might be?