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Nov 15, 2019 at 22:11 comment added Gerry Myerson And at that question also you are being encouraged to look at Morse Theory. Maybe there's no easier way to answer your question. It happens sometimes that simple-sounding questions have difficult answers.
Nov 15, 2019 at 22:06 comment added MyCindy2012 @GerryMyerson: Thanks for your suggestion. I read some references and it seems beyond my grasp right now. I think to this question, some counterexamples are pointed out. The function I actually encountered is described here math.stackexchange.com/questions/3434922/…
Nov 15, 2019 at 11:54 comment added Gerry Myerson So, have you had a look at any Morse Theory reference?
Nov 14, 2019 at 23:22 history closed Michael Hoppe
metamorphy
Paul Frost
Suzet
RRL real-analysis
Duplicate of At unique critical point, does local max imply global max?
Nov 14, 2019 at 12:05 review Close votes
Nov 14, 2019 at 23:25
Nov 14, 2019 at 11:47 comment added Gerry Myerson Maybe elib.mi.sanu.ac.rs/files/journals/tm/27/tm1427.pdf is a good reference. The first paragraph on the second page seems to imply an answer.
Nov 14, 2019 at 4:00 vote accept MyCindy2012
Nov 14, 2019 at 1:08 answer added kimchi lover timeline score: 1
Nov 14, 2019 at 0:41 comment added eyeballfrog how are you defining saddle point here
Nov 14, 2019 at 0:40 comment added Gerry Myerson I think this can be answered using Morse Theory but you'll have to find an intro-level exposition to see the application. en.wikipedia.org/wiki/Morse_theory
Nov 14, 2019 at 0:24 history asked MyCindy2012 CC BY-SA 4.0