Geodesic
On Characterizing Classes of Functions in Terms of Associated Sets
Canadian mathematical bulletin, Tome 10 (1967) no. 2, pp. 227-231

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Let κ be a class of real valued functions defined on an interval which need not be bounded. The class κ is said to be characterized in terms of associated sets if there exists a family of sets of real numbers P such that f ∈ κ if and only if for every real number α the sets a remembers of P. Many classes of functions have been characterized in terms of associated sets. The chart below summarizes a few such characterizations. 
Bruckner, A. M. On Characterizing Classes of Functions in Terms of Associated Sets. Canadian mathematical bulletin, Tome 10 (1967) no. 2, pp. 227-231. doi: 10.4153/CMB-1967-020-8
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     author = {Bruckner, A. M.},
     title = {On {Characterizing} {Classes} of {Functions} in {Terms} of {Associated} {Sets}},
     journal = {Canadian mathematical bulletin},
     pages = {227--231},
     year = {1967},
     volume = {10},
     number = {2},
     doi = {10.4153/CMB-1967-020-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1967-020-8/}
}
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