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Advanced Engineering Mathematics
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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(i) Note that So, both (ii) Take are Hence Y ft (Py) = 4x #²¹ (Y) = x => Note that are So, bet Note that て, in c. elements of 7. (vi) Vi n n vi i=1 are f~¹ (ñ vi) i=1 f" (^v₂). are open in Y. for i=1,2,.n = is also open in Y. open E T n in Yo i=1 f-1 (vi) て ñ f' (Vi) also in Z. i=1 (1) Hence, Take =) Hence, f~l (Vi) for it I So, are Vi elements of to are But note that (as arbitary union of open sets is open) Hence open in y U Vi open in Y. "EI Eて fr ( U vi) = e ¡EI as for ¡EI U f¯`¹ (vi) = IEI U f¹ (vi) € T €て itI is f (U_Vi) て topology on x it satisfies (i), (ii), (îïï).
Transcribed Image Text:(i) Note that So, both (ii) Take are Hence Y ft (Py) = 4x #²¹ (Y) = x => Note that are So, bet Note that て, in c. elements of 7. (vi) Vi n n vi i=1 are f~¹ (ñ vi) i=1 f" (^v₂). are open in Y. for i=1,2,.n = is also open in Y. open E T n in Yo i=1 f-1 (vi) て ñ f' (Vi) also in Z. i=1 (1) Hence, Take =) Hence, f~l (Vi) for it I So, are Vi elements of to are But note that (as arbitary union of open sets is open) Hence open in y U Vi open in Y. "EI Eて fr ( U vi) = e ¡EI as for ¡EI U f¯`¹ (vi) = IEI U f¹ (vi) € T €て itI is f (U_Vi) て topology on x it satisfies (i), (ii), (îïï).
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