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

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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