关于序列覆盖K映射的注记.pdfVIP

东 莞 理 工 学 院 学 报 第l5卷第3期 JOURNAL OF DONGGUAN UNⅣERSnY OF TECHNOLOGY V0I．15 No．3 2008年6月 Jun． 2008 A Note on Sequence—Covering k—Mappings xu Qing-yuan LI Jin-jin (Department of Computer Science，Zhangzhou Normal University，Zhangzhou 363000，China) Abstract In this note，it is shown that iff： ÷y is a sequence-covering k-mapping and X is a metric space， then f is a 1-sequence-covering mapping．In addition，an example is provided to show a mapping which is a sequential quotient k-mapping，but not sequence-covering，with metric domain． Key words 1-sequence··covering mapping；sequence··covering mapping；sequential quotient mapping； k-mapping；metric space In reference【l】，we gave internal characterizations of the 1-sequence—covering k-images of metric spaces and the sequence-covering k—images of metric spaces by means of sn—covers and -covers， respectively．In addition，we showed that a space is a 1-sequence—covering k-image of a metric space if and only ifX is a sequence-covering k-image of a metric space，This suggests the question：iff： Y is a sequence-covering k-mapping and is a metric space，then is f a l-sequence—covering mapping? The purpose of this note is to give an answer the question． We recall some basic definitions． Definition 1 Letf： Ybe a map． (1)fis a k-map忙’if／ is compact inX for any compact subset K ofY．Such a map ofreference 【3】is called compact． (2)f is a 1-sequence-covering map if for each y E y，there exists x ef )such that for each convergent sequence 一)in YwithY一 Y，there exists x—ef 一)with x一 x． (3)f is a sequence—covering map if each convergent sequence of Y is the image of some convergent sequence ofX． (4)f is a sequential quot