Abstract: 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.

Key words: fuzzy topology, stratified [L]-convergence space, locally bounded（compact）, locally bounded（compact） modification, coreflective subcategory

摘要： 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。

关键词: 模糊拓扑, 满层[L]-收敛空间, 局部有界（紧）, 局部有界（紧）修正, 余反射子范畴