4) If X is a non-empty Baire space, which is Hausdorff and without isolated points. If (Y, d) is a metric space and f: X→Y is a map, show that Cont (f) = {x X| f is continuous at X}, the set of points in X at which is continuous, cannot be dense and countable.
4) If X is a non-empty Baire space, which is Hausdorff and without isolated points. If (Y, d) is a metric space and f: X→Y is a map, show that Cont (f) = {x X| f is continuous at X}, the set of points in X at which is continuous, cannot be dense and countable.
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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Exercise 3
Part 4
![4) If X is a non-empty Baire space, which is Hausdorff and without isolated points. If (Y, d) is a
metric space and f: X→ Y is a map, show that
Cont (f) = {x X| f is continuous at X},
the set of points in X at which
is continuous, cannot be dense and countable.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa68164dd-6bba-4aa5-92bc-4824a71db092%2Fbf370569-3123-45e6-843c-013cc41336b5%2Flqc3pe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4) If X is a non-empty Baire space, which is Hausdorff and without isolated points. If (Y, d) is a
metric space and f: X→ Y is a map, show that
Cont (f) = {x X| f is continuous at X},
the set of points in X at which
is continuous, cannot be dense and countable.
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