Geodesic
Discontinuous Functions with the Darboux Property
Canadian mathematical bulletin, Tome 2 (1959) no. 2, pp. 111-118

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If f(x) is real-valued and continuous, it has the property that it takes on all intermediate values when it passes from one value to another. This means that whenever f(x1) and f(x2) are different and u is any number between them, then f(x) = u for at least one x between x1 and x2. We shall call this the Darboux property. 
Halperin, Israel. Discontinuous Functions with the Darboux Property. Canadian mathematical bulletin, Tome 2 (1959) no. 2, pp. 111-118. doi: 10.4153/CMB-1959-016-1
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     author = {Halperin, Israel},
     title = {Discontinuous {Functions} with the {Darboux} {Property}},
     journal = {Canadian mathematical bulletin},
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     year = {1959},
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     number = {2},
     doi = {10.4153/CMB-1959-016-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1959-016-1/}
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