Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 1994 • Question 1

Question

Math 6510 • Differentiable Manifolds Fall 1994 • Question 1

Let \(A\) and \(B\) be disjoint closed subsets of a topological space \(X\). Then there exists a continuous function \(f:X\to [0,1]\) so that \(f(A)=0\) and \(f(B)=1\).

Raw LaTeX

Let \(A\) and \(B\) be disjoint closed subsets of a topological space
\(X\). Then there exists a continuous function \(f:X\to[0,1]\) so that \(f(A)=0\) and
\(f(B)=1\).

Topic Tags

Point-Set Topology and Separation Theorems