(e) f is continuous and closed but not open. (f) f is open and closed but not continuous.
(e) f is continuous and closed but not open. (f) f is open and closed but not continuous.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please answer e and f only
Transcribed Image Text:2-5. For each of the following properties, give an example consisting of two sub-
sets X, Y CR2, both considered as topological spaces with their Euclidean
topologies, together with a map f: X → Y that has the indicated property.
(a) f is open but neither closed nor continuous.
(b) f is closed but neither open nor continuous.
(c) f is continuous but neither open nor closed.
(d) f is continuous and open but not closed.
(e) f is continuous and closed but not open.
(f) f is open and closed but not continuous.
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