THE POINTWISE LIMIT OF SEPARATELY CONTINUOUS FUNCTIONS

被引：0

作者：

Vallin, Robert W. ^{[1
]}

机构：

[1] Slippery Rock Univ, Dept Math, Slippery Rock, PA 16057 USA

来源：

REAL ANALYSIS EXCHANGE | 2008年 / 34卷 / 01期

关键词：

pointwise limit; separate continuity; joint continuity; porous sets;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The motivation for this paper is due to a question from Z. Piotrowski on whether or not the "salt-and-pepper" function in the plane was the pointwise limit of separately continuous functions. In this paper we answer that question and then go on to investigate the sets D in the plane such that chi(D) is the pointwise limit of separately continuous functions. We also look at all pointwise limits of separately continuous functions and their place in the space of Baire Class 2 functions.

引用

页码：139 / 146

页数：8

共 50 条

[21] BAIRE MEASURABILITY OF SEPARATELY CONTINUOUS-FUNCTIONS
VERA, G
QUARTERLY JOURNAL OF MATHEMATICS, 1988, 39 (153): : 109 - 116
[22] ON BAIRE CLASSIFICATION OF STRONGLY SEPARATELY CONTINUOUS FUNCTIONS
Karlova, Olena
REAL ANALYSIS EXCHANGE, 2014, 40 (02) : 371 - 381
[23] Separately continuous functions with respect to a variable frame
Herasymchuk V.H.
Maslyuchenko V.K.
Maslyuchenko O.V.
Ukrainian Mathematical Journal, 2004, 56 (9) : 1526 - 1531
[24] STRONGLY SEPARATELY CONTINUOUS AND SEPARATELY QUASICONTINUOUS FUNCTIONS f : l(2) -> R
Visnyai, Tomas
REAL ANALYSIS EXCHANGE, 2012, 38 (02) : 499 - 510
[25] POINTWISE COMPACTNESS IN SPACES OF CONTINUOUS-FUNCTIONS
ORIHUELA, J
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1987, 36 : 143 - 152
[26] POINTWISE CONVERGENCE THEOREM FOR SEQUENCES OF CONTINUOUS FUNCTIONS
SCHRADER, K
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1971, 159 (NSEP) : 155 - &
[27] Approximation by pointwise bounded sets of continuous functions
Ferrando, Juan Carlos
TOPOLOGY AND ITS APPLICATIONS, 2022, 317
[28] Diagonals of separately pointwise Lipschitz mappings
Mykhaylyuk V.V.
Sobchuk O.V.
Journal of Mathematical Sciences, 2014, 196 (5) : 652 - 664
[29] Compact spaces of separately continuous functions in two variables
Gul'ko, SP
Sokolov, GA
TOPOLOGY AND ITS APPLICATIONS, 2000, 107 (1-2) : 89 - 96
[30] Quasicontinuous and separately continuous functions with values in Maslyuchenko spaces
Banakh, Taras
TOPOLOGY AND ITS APPLICATIONS, 2017, 230 : 353 - 372

← 1 2 3 4 5 →