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.
