Suppose that F: M N is a continuous bijection and M is covering compact. Show directly that F is a homeomorphism. (Do not use the proofs we gave that covering compact is equivalent to sequentially compact or that this is true for sequentially compact spaces. There is a much easier direct argument.)
Suppose that F: M N is a continuous bijection and M is covering compact. Show directly that F is a homeomorphism. (Do not use the proofs we gave that covering compact is equivalent to sequentially compact or that this is true for sequentially compact spaces. There is a much easier direct argument.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Transcribed Image Text:4. Suppose that F: M N is a continuous bijection and M is covering compact. Show
directly that F is a homeomorphism. (Do not use the proofs we gave that covering
compact is equivalent to sequentially compact or that this is true for sequentially
compact spaces. There is a much easier direct argument.)
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