拓扑空间偶范畴中的同伦正则态射
On Homotopy Regular Morphism in the Category of Topological Pairs
摘要:
本文将点标拓扑空间范畴中的同伦单、同伦满和同伦正则态射等概念推广到拓扑空间偶范畴的情形。研究了在中,同伦正则态射存在的条件、性质以及它与同伦单(满)态和同伦等价之间的关系。
Abstract: In this paper, the concepts of homotopy monomorphism (epimorphism) and homotopy regular morphism in the category of topological space with base point are generalized to the category of topological pairs . The paper studies the conditions and properties of homotopy regular morphism and the relationships between homotopy monomorphism (epimorphism) and homotopy equivalent morphism in .
参考文献
[1]
|
S. T. Hu. Homotopy theory. New York: Academic Press, 1959.
|
[2]
|
P. Hilton. Homotopy theory and duality. New York: Gorelen and Breach, 1965.
|
[3]
|
T. Ganea. On monomorphisms in homotopy theory. Topology, 1976, 6 (2): 149-152.
|
[4]
|
M. Mather. Homotopy monomorphisms and homotopy pushouts. Topology and its Applications, 1997, 81(2): 159-162.
|
[5]
|
G. Mnklerjee. Equivalent homotopy epimorphisms homotopy monomorphisms and homotopy equivalence. Bulletin of the Belgian Mathemati- cal Society, 1995, 2(4): 447-461.
|
[6]
|
W. H. Shen, Z. S. Zou. Semilocalization of epimorphisms and monomorphisms in homotopy theory. Topology and Its Applications, 1998, 88(3): 207-217.
|
[7]
|
冯良贵. 因式分解范畴[J]. 数学研究与评论, 1996, 16(2): 281-284.
|
[8]
|
曹永知, 郭驼英, 朱萍. 关于同伦正则态射[J]. 数学物理学报, 2000, 20(2): 274-277.
|
[9]
|
钱丽华, 钱有华. 同伦正则态射的注记[J]. 宁波大学学报(理工版), 2005, 18(4): 428-431.
|
[10]
|
王凯华, 陈胜敏, 钱有华. 同伦正则态射的若干性质[J]. 浙江师范大学学报(自然科学版), 2006, 29(3): 258-261.
|
[11]
|
钱有华, 陈胜敏. 同纬映象函子与同伦正则态射[J]. 吉林大学学报(理学版), 2009, 47(3): 476-480.
|
[12]
|
王向辉, 王玉玉. 有限CW复形间的稳定同伦正则态射[J]. 南开大学学报(自然科学版), 2011, 44(5): 34-40.
|
[13]
|
沈信耀. 同调论[M]. 北京: 科学出版社, 2002.
|