Watch uniform convergence fail: xⁿ on [0, 1]
Sequences and Series of FunctionsAnalysis & Linear Algebrafree
Every point drops to 0, yet the sup distance never shrinks — see the trouble slide toward 1, then cut the interval and watch it turn uniform.
Sequences and Series of FunctionsAnalysis & Linear Algebrafree
Every point drops to 0, yet the sup distance never shrinks — see the trouble slide toward 1, then cut the interval and watch it turn uniform.