Consider X={a,b,c} and the following topologies: τ_1={X,∅,{a},{a,b}} τ_2={X,∅,{b},{a,b}} a) Let f:Xτ_1→Xτ_1 such that f({a})={b,c}. Is f a continuous function? yes, no or can't you tell? b) Let g:Xτ_1 →Xτ_2 such that g({b})={b,c}. Is g a continuous function? yes, no or can't you tell? Justify your answer
Consider X={a,b,c} and the following topologies: τ_1={X,∅,{a},{a,b}} τ_2={X,∅,{b},{a,b}} a) Let f:Xτ_1→Xτ_1 such that f({a})={b,c}. Is f a continuous function? yes, no or can't you tell? b) Let g:Xτ_1 →Xτ_2 such that g({b})={b,c}. Is g a continuous function? yes, no or can't you tell? Justify your answer
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.
Chapter6: Applications Of The Derivative
Section6.CR: Chapter 6 Review
Problem 3CR
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Consider X={a,b,c} and the following topologies:
τ_1={X,∅,{a},{a,b}}
τ_2={X,∅,{b},{a,b}}
a) Let f:Xτ_1→Xτ_1 such that f({a})={b,c}. Is f a continuous function? yes, no or can't you tell?
b) Let g:Xτ_1 →Xτ_2 such that g({b})={b,c}. Is g a continuous function? yes, no or can't you tell?
Justify your answer
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