指出了几种局部凸拓扑的完整性与感应拓扑的完整性之间的关系。
The relation between the completeness of several local convex topology and that of induction topology was pointed out in this paper.
从几何和凸集的角度，系统地给出了平面闭参数曲线全局凸和局部凸定义，并且证明了这两个定义是等价的。
Based on geometry and convex set methods, this paper gives systemically the definitions of global and local convexity for planar closed parametric curve, and proves the two definitions are equivalent.
依据参数曲线凸性的原始几何定义，讨论了参数曲线的局部凸和全局凸性，得到了参数曲线局部凸和全局凸的若干性质。
Based on the original geometrical definition of the convexity for planar parametric curve, the local and global convexity are discussed, and a few properties are obtained.
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