WHICH TOPOLOGIES ARE QUASIMETRIZABLE

被引：6

作者：

KOPPERMAN, RD ^{[1
]}

机构：

[1] CUNY CITY COLL,DEPT MATH,NEW YORK,NY 10031

来源：

TOPOLOGY AND ITS APPLICATIONS | 1993年 / 52卷 / 02期

关键词：

QUASIMETRIZABLE; CONJUGATE; ENCLOSING SET RELATION; PAIR BASE; PAIR GENERATOR; (SELF-SIGMA) COCUSHIONED; (LOCAL) QUASIUNIFORMITY; SIGMA-ALEXANDROFF SPACE;

D O I：

10.1016/0166-8641(93)90029-D

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A characterization of quasimetrizable spaces is given; they are those whose topologies arise from a sigma-self-cocushioned pairbase whose dual is sigma-self-cocushioned. This is closely related to the known characterization of gamma-spaces as those whose topologies arise from a sigma-self-cocushioned pairbase (with no dual condition). The last section of the paper discusses to what extent this is a topological characterization of quasimetrizability, and notes the absence of a ''Bing-style'' characterization.

引用

页码：99 / 107

页数：9

共 25 条

[1] METRIZATION OF TOPOLOGICAL SPACES [J].

BING, RH .

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1951, 3 (02) :175-186

[2]

Fletcher P., 1982, LECT NOTES PURE APPL, V77

[3]

FLETCHER P, 1972, J MATH ANAL APPL, V39, P363

[4]

Fox R., METRIZABILITY QUASIM

[5]

GRUENHAGE G, 1983, HDB SET THEORETIC TO, P423

[6] A GENERAL-THEORY OF STRUCTURE SPACES WITH APPLICATIONS TO SPACES OF PRIME IDEALS [J].

HENRIKSEN, M ;

KOPPERMAN, R .

ALGEBRA UNIVERSALIS, 1991, 28 (03) :349-376

[7]

HENRIKSEN M, 1990, GENERAL TOPOLOGY APP, P133

[8]

Kelley J.L., 1955, GEN TOPOLOGY

[9]

Kelly J. C., 1963, P LOND MATH SOC, V13, P71, DOI [DOI 10.1112/PLMS/S3-13.1.71, 10.1112/plms/s3-13.1.71]

[10] COMPUTER-GRAPHICS AND CONNECTED TOPOLOGIES ON FINITE ORDERED SETS [J].

KHALIMSKY, E ;

KOPPERMAN, R ;

MEYER, PR .

TOPOLOGY AND ITS APPLICATIONS, 1990, 36 (01) :1-17

← 1 2 3 →