双层空间的刻画

数学物理学报 ›› 2010, Vol. 30 ›› Issue (3): 649-655.

双层空间的刻画

李克典

漳州师范学院数学系福建漳州 363000

收稿日期:2008-11-13 修回日期:2009-12-28 出版日期:2010-05-25 发布日期:2010-05-25
基金资助:
国家自然科学基金(10571151, 10671173)和福建省自然科学基金(2006J0228, 2008F5066)资助

Characterizations of Pairwise Stratifiable Spaces

LI Ke-Dian

Department of Mathematics, Zhangzhou Normal University, Fujian Zhangzhou 363000

Received:2008-11-13 Revised:2009-12-28 Online:2010-05-25 Published:2010-05-25
Supported by:
国家自然科学基金(10571151, 10671173)和福建省自然科学基金(2006J0228, 2008F5066)资助

摘要/Abstract

摘要：

该文利用双 $g$ -函数和半连续函数给出了双层空间的刻画, 得到: 空间 (X, τ₁, τ₂) 是双层当且仅当对于每一个f ∈ τ_i- LSC(X), 都对应一个h(f) ∈τ_i-LSC(X)∩τ_j- USC(X) 使得

(1) 0≤ h(f)≤ f 且当 f(x)>0 时, 0<h(f)(x)(x).

(2) 当 f≤ f' 时, h(f)≤ h(f').

关键词: 双层空间, 双拓扑空间, 双单调正规空间, 上半连续映射, 下半连续映射

Abstract:

In this paper, we give some characterizations of pairwise stratifiable spaces by means of pairwise g-functions and semi-continuous functions.
It is established that: a space (X, τ₁, τ₂) is pairwise stratifiable if and only if for each f ∈ τ_i- LSC(X), one assigns an h(f) ∈τ_i-LSC(X)∩τ_j- USC(X) such that.

(1) 0≤ h(f)≤ f and 0<h(f)(x)(x) whenever f(x)>0 .

(2) h(f)≤ h(f') whenever f≤ f' .

Key words: Pairwise stratifiable spaces, Bitopological spaces, Pairwise monotonically space, Upper semi-continuous maps, Lower semi-continuous maps

中图分类号:

54E20

李克典. 双层空间的刻画[J]. 数学物理学报, 2010, 30(3): 649-655.

LI Ke-Dian. Characterizations of Pairwise Stratifiable Spaces[J]. Acta mathematica scientia,Series A, 2010, 30(3): 649-655.

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