CAJ | 학술논문

建立在一般拓扑空间中存在连续函数使得它的支撑在某个开集内、在开集的某个闭子集上恒为常数的充要条件。同时，在一般拓扑空间中的完美覆盖上建立Urysohn引理，将该定理推广到更加一般的形式，建立子集函数分离的充要条件。文章利用保序定理证明更一般的Urysohn引理，得到集族是完美覆盖的充要条件。同时阐述各种形式的Urysohn引理的联系，得到完美覆盖的重要性质。最后给出 Urysohn 引理的应用，证明推广的Tietze扩张定理。
건립재일반탁복공간중존재련속함수사득타적지탱재모개개집내、재개집적모개폐자집상항위상수적충요조건。동시，재일반탁복공간중적완미복개상건립Urysohn인리，장해정리추엄도경가일반적형식，건립자집함수분리적충요조건。문장이용보서정리증명경일반적Urysohn인리，득도집족시완미복개적충요조건。동시천술각충형식적Urysohn인리적련계，득도완미복개적중요성질。최후급출 Urysohn 인리적응용，증명추엄적Tietze확장정리。
We present the sufficient and necessary conditions that there is continuous functions which supports is contained in cer-tain open set and the value is constant in some closed subset of the open set. At the same time, we establish Urysohn lemma in the per-fect Cover of general topological space and obtain a more general form of this theorem and construct the sufficient and necessary condi-tions which the sets are function separared. order preserving theory is utilized to prove a more general Uryshon Lemma and we obtain the sufficient and necessary conditions which a set family is a perfect cover. Then we survey the connection between the various Ury-sohn’s lemmas and obtain an important property of perfect cover. Finally, we give the application of Urysohn lemma and prove the gen-eralized Tietze expansion theorem.