Metamath Proof Explorer

Table of Contents - 20.3.14. Topology and algebraic structures

1. The norm on the ring of the integer numbers
   1. zringnm
   2. zzsnm
2. Topological ` ZZ ` -modules
   1. zlm0
   2. zlm1
   3. zlmds
   4. zlmtset
   5. zlmnm
   6. zhmnrg
   7. nmmulg
   8. zrhnm
   9. cnzh
   10. rezh
3. Canonical embedding of the field of the rational numbers into a division ring
   1. cqqh
   2. df-qqh
   3. qqhval
   4. zrhf1ker
   5. zrhchr
   6. zrhker
   7. zrhunitpreima
   8. elzrhunit
   9. elzdif0
   10. qqhval2lem
   11. qqhval2
   12. qqhvval
   13. qqh0
   14. qqh1
   15. qqhf
   16. qqhvq
   17. qqhghm
   18. qqhrhm
   19. qqhnm
   20. qqhcn
   21. qqhucn
4. Canonical embedding of the real numbers into a complete ordered field
   1. crrh
   2. crrext
   3. df-rrh
   4. rrhval
   5. rrhcn
   6. rrhf
   7. df-rrext
   8. isrrext
   9. rrextnrg
   10. rrextdrg
   11. rrextnlm
   12. rrextchr
   13. rrextcusp
   14. rrexttps
   15. rrexthaus
   16. rrextust
   17. rerrext
   18. cnrrext
   19. qqtopn
   20. rrhfe
   21. rrhcne
   22. rrhqima
   23. rrh0
5. Embedding from the extended real numbers into a complete lattice
   1. cxrh
   2. df-xrh
   3. xrhval
6. Canonical embeddings into the ordered field of the real numbers
   1. zrhre
   2. qqhre
   3. rrhre
7. Topological Manifolds
   1. cmntop
   2. df-mntop
   3. relmntop
   4. ismntoplly
   5. ismntop