[b]证明[/b].[tex=1.857x1.357]Fuvm9Mwml7lIOgc0vriwJw==[/tex]在有界闭集[tex=0.643x1.0]+oHlSEIghohvxH3XmTRlFg==[/tex]上连续.[tex=2.5x1.071]7LdKmkSlODqVFlKBvNmN9LeZwBAE29wNm0PE1lji1ic=[/tex]，有[tex=2.714x1.214]GhEVJkIAfaWbV0HCIYz25gSEiIoUEJ+WzsXljh6QOi4=[/tex]使[tex=7.5x1.429]2PQrKYf2QqJftiTGSMCH3A1UqPGKcyICLghVCjzonvloXq8a8oaPzKl4h6iepORAc3s5VwrK9cEVhNd2uqHN7A==[/tex]有[tex=7.429x1.429]6efEJKyolHVGSBh/smh3NqZ+ejHO3T3tv6+ZaB/udVeDxdyIA3K5lFzh/dnGgi/hyRbFzxqFlpvDML/meHrEEg==[/tex]又[tex=6.714x2.786]FMibfz/lYIFRI8YldoYAzQO6NLKflm3rwfBN49PsrXtmZigCPOrzig8cQ8dupOHsCE//viJ84oVd2wk0AHV1xw==[/tex]，于是由有限覆盖定理，有[tex=2.714x1.071]RAvkFded88hNlpK25JZL9Q==[/tex]使[tex=6.643x3.286]FMibfz/lYIFRI8YldoYAzTbF7nGDDuHpukXQOlRdR61ETfqphZkUmysjkQeCvmXe1slEuZWD9EIXXtaWzlzS8XSXTQW7NQ0taXSnkDthNB4=[/tex].于是有[tex=3.571x1.357]6S5OJPbrzPs93vkpiRzC/fI6bB6wtqPgrHHRmilON5gkmCaSmOHMM6CtEXGJLB2C[/tex][tex=6.429x3.286]03TO/vRNjt97C279tKizseBvNTpfeTidTiUaOBarIzv3of3720k2yK4BaK+iZN+bHqLev+YcaNNJF7lNfnuqmQ==[/tex].后者有界.