Matthew Wiener once explained to me that because of the close connections between forcing and the Baire category theorem, forcing could be used to prove certain results in analysis that are more commonly proved via BCT. Unfortunately, I can't remember the details, and the closest thingall I've been able to find is this articlethis article where Wiener states that there is an easysketches a proof via forcing of the existence of continuous nowhere-differentiable functions of Hausdorff dimension one. Perhaps some other MO reader can supply the missing details.
Matthew Wiener once explained to me that because of the close connections between forcing and the Baire category theorem, forcing could be used to prove certain results in analysis that are more commonly proved via BCT. Unfortunately, I can't remember the details, and the closest thing I've been able to find is this article where Wiener states that there is an easy proof via forcing of the existence of continuous nowhere-differentiable functions of Hausdorff dimension one. Perhaps some other MO reader can supply the missing details.
Matthew Wiener once explained to me that because of the close connections between forcing and the Baire category theorem, forcing could be used to prove certain results in analysis that are more commonly proved via BCT. Unfortunately, all I've been able to find is this article where Wiener sketches a proof via forcing of the existence of continuous nowhere-differentiable functions of Hausdorff dimension one. Perhaps some other MO reader can supply the missing details.
Matthew Wiener once explained to me that because of the close connections between forcing and the Baire category theorem, forcing could be used to prove certain results in analysis that are more commonly proved via BCT. Unfortunately, I can't remember the details, and the closest thing I've been able to find is this article where Wiener states that there is an easy proof via forcing of the existence of continuous nowhere-differentiable functions of Hausdorff dimension one. Perhaps some other MO reader can supply the missing details.