A SURVEY OF CLEAVABILITY

被引：13

作者：

ARHANGELSKII, AV ^{[1
]}

机构：

[1] MOSCOW MV LOMONOSOV STATE UNIV,DEPT MATH & MECH,MOSCOW 119899,RUSSIA

来源：

TOPOLOGY AND ITS APPLICATIONS | 1993年 / 54卷 / 1-3期

关键词：

CLEAVABILITY; C-THICK SPACE; C-SIMPLE SPACE; CONNECTED SPACE; ARCWISE CONNECTEDNESS; MANIFOLD; G-DELTA-DIAGONAL; METRIZABLE SPACE; Q-SPACE; POLYHEDRON; STRONGLY SIGMA-DISCRETE SPACE; HILBERT SPACE; EUCLIDEAN SPACE; REAL LINE; PARACOMPACT P-SPACE; LINDELOF SPACE; DIMENSION; LOCALLY CONNECTED SPACE; ONE-TO-ONE CONTINUOUS MAPPING; LOTS;

D O I：

10.1016/0166-8641(93)90058-L

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A space X is said to be cleavable over a class of spaces P if for every subset A of X there exist a space Y is-an-element-of P and a continuous mapping f : X --> Y such that f(A) and f(X - A) are disjoint and f(X) = Y. If X is cleavable over the class of all subspaces of a space Y, then Y is said to be cleavable over Y. Cleavability may be treated as a relativization of one-to-one continuous mappings. This paper is a survey which covers the first six years of the theory of cleavability. In particular, results on cleavability over the Hilbert space R(omega), the Euclidean spaces R(n), the real line R, the space Q of rational numbers and the space J of irrational numbers are presented.

引用

页码：141 / 163

页数：23

共 23 条

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