Let X= [0, 6], T1 and 72 be the standard and the discrete topologies on X respectively. Suppose f: X X is given by f(x)= = X X if x = [0,3). if x = [3,6]. i. Sketch the graph of f. ii. Show that f is continuous if T2 is the topology on the domain of f and T1 is that on the codomain. iii. Demonstrate that f is discontinuous if 71 is the topology on the domain of f and T2 is that on the codomain.
Let X= [0, 6], T1 and 72 be the standard and the discrete topologies on X respectively. Suppose f: X X is given by f(x)= = X X if x = [0,3). if x = [3,6]. i. Sketch the graph of f. ii. Show that f is continuous if T2 is the topology on the domain of f and T1 is that on the codomain. iii. Demonstrate that f is discontinuous if 71 is the topology on the domain of f and T2 is that on the codomain.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.CR: Chapter 3 Review
Problem 2CR
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![Let X= [0, 6], 71 and 72 be the standard and the discrete topologies on X
respectively. Suppose f: X→ X is given by
f(x) =
-
X
X
if x = [0,3).
if x = [3,6].
i. Sketch the graph of f.
ii. Show that f is continuous if T2 is the topology on the domain of f and 71
is that on the codomain.
iii. Demonstrate that f is discontinuous if 71 is the topology on the domain
of f and T2 is that on the codomain.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F425ee8a1-7c2f-4657-9e12-faf7ddcef3f4%2F308d1867-8458-44da-8ce0-08bf14cf1b9c%2Ffcyut9f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let X= [0, 6], 71 and 72 be the standard and the discrete topologies on X
respectively. Suppose f: X→ X is given by
f(x) =
-
X
X
if x = [0,3).
if x = [3,6].
i. Sketch the graph of f.
ii. Show that f is continuous if T2 is the topology on the domain of f and 71
is that on the codomain.
iii. Demonstrate that f is discontinuous if 71 is the topology on the domain
of f and T2 is that on the codomain.
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