摘要
本論文主要討論集值三角多項式與集值連續週期函數的一些關係，一開始 先定義一些Hausdorff距離的意義與符號，然後再探討相關的性質與引理。 在最後一小節中，我們嘗試在Hausdoff距離下去推廣Weierstrass approxim- .ation theorem 在集值函數的狀況下，所帶給我們的結果。由於Weierstrass approximation theorem 在Hausdorff 距離下可以成立，我們也就可以證明Weierstrass approximation theorem by trigonometric polynomials 也會在Hausdorff 距離之下是成立的。
並列摘要
In this paper, we inverstigate the relation between set-valued periodic cotinuous functions and set-valued trigonometric polynomials. We give the definition of some basic properties of the Hausdorff distance. Then, we generalized the Weierstrass Apporximation Theorem by trigonometric polynomials to the set-valued case. The set-valued generalizeation of Weierstrass approximation Theorem by polynomials has been established by HSU[6]. Taking use of the result, we show the set-valued generalization of Weierstrass approximation Theorem by trigonometric polynomials without any Aumann integers(c.f. WU[7]).