CAJ | 학술논문

对满层L-收敛空间引入了有界集（紧集）和局部有界（紧）空间的概念，它们可以看作J?ger相应概念的推广。证明了：（1）广义Lowen函子（收敛空间范畴可以通过广义Lowen函子余反射嵌入到满层 L-收敛空间范畴）保持并且反射有界（紧）性和局部有界（紧）性；（2）局部有界（紧）的满层L-收敛空间是满层L-收敛空间的余反射子范畴。
대만층L-수렴공간인입료유계집（긴집）화국부유계（긴）공간적개념，타문가이간작J?ger상응개념적추엄。증명료：（1）엄의Lowen함자（수렴공간범주가이통과엄의Lowen함자여반사감입도만층 L-수렴공간범주）보지병차반사유계（긴）성화국부유계（긴）성；（2）국부유계（긴）적만층L-수렴공간시만층L-수렴공간적여반사자범주。
For stratified L-convergence spaces, the notions of bounded(compacted)set and locally bounded(compacted) space are introduced. These notions can be regarded as the natural extensions of J?ger’s corresponding notions. It is proved that(1)the general Lowen functor(by which the category of convergence spaces embeds coreflectively into the category of stratified L-convergence spaces)both preserves and reflects boundedness(compact)and locally boundedness (compact);(2)the category of locally bounded(compacted)stratified L-convergence spaces is a coreflective subcategory of the category of stratified L-convergence spaces.