Fronts and lexicographically well-orderer

[HyacinthH]

Hi everyone!

I have a problem with these lemmas(II.2.18 and II.2.22, front from Nash-William theory). I know it is probably simple, but my brain can't find any good solution to prove it. I got a headache from it haha . Can please someone explains it to me? Thanks for all answers! I tried to do something with it, but nothing with i can share, because I get totally nothing

 

[Deleted member 4993]

Hi everyone!

I have a problem with these lemmas(II.2.18 and II.2.22, front from Nash-William theory). I know it is probably simple, but my brain can't find any good solution to prove it. I got a headache from it haha . Can please someone explains it to me? Thanks for all answers! I tried to do something with it, but nothing with i can share, because I get totally nothing
View attachment 28735

Please define for us, from your textbook or class-notes or Google:

• Fronts on the domain
  
• lexicographical rank
  
  

 

[HyacinthH]

Thanks, for the answer. I will send definition of front, but in my textbook there is nothing about lexicographical rank. It says only that "Every front is lexicographically well-ordered" nothing more. This square subset means that s is an initial segment of t.