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

[1] The pointwise limit of holomorphic functions
Krantz, Steven G.
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2023, 68 (12) : 2144 - 2147
[2] SEPARATELY CONTINUOUS FUNCTIONS ARE BAIRE FUNCTIONS
CARROLL, FW
AMERICAN MATHEMATICAL MONTHLY, 1971, 78 (02): : 175 - &
[3] A CONTINUOUS TALE ON CONTINUOUS AND SEPARATELY CONTINUOUS FUNCTIONS
Ciesielski, Krzysztof Chris
Miller, David
REAL ANALYSIS EXCHANGE, 2016, 41 (01) : 19 - 54
[4] On monotonous separately continuous functions
Grushka, Yaroslav, I
APPLIED GENERAL TOPOLOGY, 2019, 20 (01): : 75 - 79
[5] ON SEPARATELY APPROXIMATELY CONTINUOUS FUNCTIONS
Grande, Zbigniew
ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING, 2010, 35 (1D): : 51 - 56
[6] SEPARATELY CONTINUOUS-FUNCTIONS
NEWMAN, DJ
MONTGOMERY, HL
FINE, NJ
GRIPENBERG, G
HENSLEY, D
KUTTLER, JR
LOSSERS, OP
MCCOY, R
NOLTIE, S
RIESE, A
SELLKE, T
SOLOMON, A
VOJTA, P
AMERICAN MATHEMATICAL MONTHLY, 1978, 85 (03): : 198 - 199
[7] On the pointwise limit of complex analytic functions
Beardon, AF
Minda, D
AMERICAN MATHEMATICAL MONTHLY, 2003, 110 (04): : 289 - 297
[8] On approximation of the separately and jointly continuous functions
Voloshyn, H. A.
Maslyuchenko, V. K.
Maslyuchenko, O., V
CARPATHIAN MATHEMATICAL PUBLICATIONS, 2010, 2 (02) : 10 - 20
[9] The topologization of the space of separately continuous functions
Voloshyn, H. A.
Maslyuchenko, V. K.
CARPATHIAN MATHEMATICAL PUBLICATIONS, 2013, 5 (02) : 199 - 207
[10] INTEGRATION OF SEPARATELY CONTINUOUS-FUNCTIONS
JANSSEN, A
MATHEMATICA SCANDINAVICA, 1981, 48 (01) : 68 - 78

← 1 2 3 4 5 →