1. If set A is compact, show that f(A) is compact. Is the converse true?
Ans. f:M to N is continuous and A subset M is compact. Then f(A) is compact.
The converse is not necessarilly true. For Ex: F(x)=0 for every x in R(real #'s) and
k={0}. Then f^-1(k)=R is not compact.
2. If...
Sorry, here goes.
1. If set A is compact, show that f(A) is compact. Is the converse true?
Ans. f:M to N is continuous and A subset M is compact. Then f(A) is compact.
The converse is not necessarilly true. For Ex: F(x)=0 for every x in R(real #'s) and
k={0}. Then f^-1(k)=R is not...
1. If set A is compact, show that f(A) is compact. Is the converse true?
2. If set A is connected, show that f(A) is connected. Is the converse true?
3. If set B is closed, show that B inverse is closed.
Any help with any or all of these three would be greatly appreciated.
Stumped!
1. If A is compact, show that f(A) is compact. Is the converse true?
2. If A is connected, show that f(A) is connected. Is the converse true?
3. If B is closed, show that B inverse is closed.
Any help with any or all of these three would be greatly appreciated.