Recent content by deanslist1411

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.