| 11. | For example, compactness and connectedness are topological properties, whereas boundedness and completeness are not.
|
| 12. | In the absence of the axiom of choice, total boundedness and precompactness must be distinguished.
|
| 13. | Clearly, this also means that boundedness is no longer equivalent to Lipschitz continuity in this context.
|
| 14. | Note that this more general concept of boundedness does not correspond to a notion of " size ".
|
| 15. | The resulting axiom schema is also called the "'axiom schema of boundedness " '.
|
| 16. | Boundedness is characteristic of perfective aspects such as the Ancient Greek stative ( " I knew " ).
|
| 17. | Progress towards boundedness in vertical strips was made by S . S . Gelbart and F . Shahidi.
|
| 18. | Depending on the additional structure defined for the category at hand ( topology, boundedness, and so on.
|
| 19. | It follows from this boundedness that the projections " P " " N " defined by
|
| 20. | That is, we define total boundedness in elementary terms but define precompactness in terms of compactness and Cauchy completion.
|