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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Spring 2020 • Question 4

Question

Math 6420 • PDE Spring 2020 • Question 4

Show that a mapping \(T:X\to Y\) where \(X\) and \(Y\) are metric spaces is continuous if and only if the inverse image of any closed set \(M\subset Y\) is a closed set in \(X\).

Raw LaTeX

Show that a mapping \(T:X\to Y\) where \(X\) and \(Y\) are metric spaces is continuous if and
only if the inverse image of any closed set \(M\subset Y\) is a closed set in \(X\).

Topic Tags

Linear Programming and Optimization Point, Continuous, and Residual Spectrum