Teaching JKPSC Lecturership Mock Test Series 2024-25 Mathematical Science Topology Topological spaces and Continuous Functions
Which of the following statements regarding topological spaces is true?
1
The open interval (0,1) in R is homeomorphic to the closed interval [0,1] in R.
2
Any two compact sets in \(R^n\) are homeomorphic.
3
Any two closed intervals of the same length in \(R^n\) are homeomorphic.
4
The set \(R^n \) \ {0} (i.e., the set of all points in \(R^n\) except the origin) is homeomorphic to the one-point compactification of \(R^n\).