a) Show that, any function f: X → Y is continuous if X have discrete topology.
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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![a) Show that, any function f: X → Y is continuous if X have discrete topology.
b) Let Ru denote the set of real numbers in lower limit topology. Is the function
f: Ru
- Ru ,
f(x) = x²
homeomorphism? Justify your claim.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc9b44cec-e758-45e2-b07e-7ac4bbf473ac%2Fb910bc76-fbef-46da-b3e4-a74f8f312d4f%2F7w7junphk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:a) Show that, any function f: X → Y is continuous if X have discrete topology.
b) Let Ru denote the set of real numbers in lower limit topology. Is the function
f: Ru
- Ru ,
f(x) = x²
homeomorphism? Justify your claim.
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