Geodesic
Boundedness in a Quasi-Uniform Space
Canadian mathematical bulletin, Tome 13 (1970) no. 3, pp. 367-370

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Although a nontopological concept, boundedness seems to be of considerable importance in a topological space. 'There are many topological problems in which it is essential to be able to make this distinction' (between bounded and unbounded sets) [1]. Boundedness and in particular boundedness-preserving' uniform spaces appear to have applications to topological dynamics [4].In spite of this importance, there have been only isolated attempts at developing the concept. Alexander [1] and Hu [7] tried the axiomatic approach. Hu, for example, calls a nonempty family of sets a boundedness if is hereditary and closed under finite union. 
Murdeshwar, M. G.; Theckedath, K. K. Boundedness in a Quasi-Uniform Space. Canadian mathematical bulletin, Tome 13 (1970) no. 3, pp. 367-370. doi: 10.4153/CMB-1970-069-5
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     title = {Boundedness in a {Quasi-Uniform} {Space}},
     journal = {Canadian mathematical bulletin},
     pages = {367--370},
     year = {1970},
     volume = {13},
     number = {3},
     doi = {10.4153/CMB-1970-069-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1970-069-5/}
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