用致密性定理统一证明其它实数连续性基本定理。
Proves the other real number continuity fundamental theorems uniformly by the compact theorem.
通过巧妙地构造辅助数列，应用致密性定理、柯西收敛准则来证明闭区间上连续函数的介值性定理。
We proved the intermediate value theorem for continuous function at closed interval by constructing auxiliary sequence ingeniously and applying compact theorem as well as Cauchy convergence criterion.
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