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continous real valued function 58) Let f be a that the set inverse image with respect to f of an on R. Show set is open open, of a closed set is closed, and of a Borel set is Borel,

continous real valued function 58) Let f be a that the set inverse image with respect to f of an on R. Show set is open open, of a closed set is closed, and of a Borel set is Borel,

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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58.) Let f be a continous real valued function on IR. Show that the set imverse image with respect to f of an open set is closed set is closed, and of a Borel set is Borel, algebra of Open Let B = {oc IR: f ¹ (0) 6B}. Prove that B' is a all containing you Here open, can use the fact from the topology continous function f: IR IR, we have f + (0) is open if I is open. a sets. Why does this complete the problem? that for a
Transcribed Image Text:58.) Let f be a continous real valued function on IR. Show that the set imverse image with respect to f of an open set is closed set is closed, and of a Borel set is Borel, algebra of Open Let B = {oc IR: f ¹ (0) 6B}. Prove that B' is a all containing you Here open, can use the fact from the topology continous function f: IR IR, we have f + (0) is open if I is open. a sets. Why does this complete the problem? that for a
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