Geodesic
Continuous Functions on the Sphere and Isometries
Canadian mathematical bulletin, Tome 12 (1969) no. 6, pp. 753-757

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The theorem of Borsuk-Ulam states that n odd functions on the n-dimensional sphere always have a common zero. We have tried to obtain a similar theorem by "slightly" changing the conditions for the functions, but it turned out that only a very weak analogue can be expected in our case. Here we want to prove a few results and mention some of the questions which have remained unanswered. 
Hadwiger, H.; Mani, P. Continuous Functions on the Sphere and Isometries. Canadian mathematical bulletin, Tome 12 (1969) no. 6, pp. 753-757. doi: 10.4153/CMB-1969-097-4
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     title = {Continuous {Functions} on the {Sphere} and {Isometries}},
     journal = {Canadian mathematical bulletin},
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     year = {1969},
     volume = {12},
     number = {6},
     doi = {10.4153/CMB-1969-097-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-097-4/}
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