Teaching CSIR NET Mock Test Series Mathematical Science Topology Topological spaces and Continuous Functions
Let X denote the topological space R with the cofinite topology (i.e., the finite complement topology) and let Y denote the topological space R with the Euclidean topology. Which of the following statements are true?
1
X × [0, 1] is closed in X × Y with respect to the product topology
2
X × [0, 1] is compact with respect to the product topology
3
X is compact
4
X × Y is compact with respect to the product topology