Consider the function $f(x,t)$ where $(x,t)\in[0,1]\times[0,1]$; I am looking for examples of such functions that are in $C\left([0,1],L_2([0,1],\mathbb{R})\right)$ with respect to either $t$ and $x$, but not in $C([0,1]\times[0,1],\mathbb{R})$.
Spaces containing a two variable functions
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real-analysis
functional-analysis
continuity
lebesgue-integral
lp-spaces
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0Can you be clearer? I can't tell what functions you want. And what does "$C\left([0,1],L_2([0,1],\mathbb{R})\right)$" mean? – 2017-02-19
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0It refers to the space that the map $t\mapsto f(\cdot,t)$ or $x\mapsto f(x,\cdot)$ belong to – 2017-02-20