Metamath Proof Explorer

Table of Contents - Generic Neighborhood Spaces

Any neighborhood space is an open set topology and any open set topology is a neighborhood space. Seifert and Threlfall define a generic neighborhood space which is a superset of what is now generally used and related concepts and the following will show that those definitions apply to elements of .

Seifert and Threlfall do not allow neighborhood spaces on the empty set while sn0top is an example of a topology with an empty base set. This divergence is unlikely to pose serious problems.

  1. gneispa
  2. gneispb
  3. gneispace2
  4. gneispace3
  5. gneispace
  6. gneispacef
  7. gneispacef2
  8. gneispacefun
  9. gneispacern
  10. gneispacern2
  11. gneispace0nelrn
  12. gneispace0nelrn2
  13. gneispace0nelrn3
  14. gneispaceel
  15. gneispaceel2
  16. gneispacess
  17. gneispacess2