A note on feebly continuous functions

被引：2
|
作者：
Leader, Imre [1 ]
机构：
[1] Ctr Math Sci, Dept Pure Math & Math Stat, Cambridge CB3 0WB, England
来源：
TOPOLOGY AND ITS APPLICATIONS | 2009年 / 156卷 / 16期
关键词：
Real analysis; Ramsey theory;
D O I：
10.1016/j.topol.2009.04.009
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A function f from R-2 to R is said to be feebly continuous at a point (x, y) if there exist sequences x(n) SE arrow x and yn SE arrow y with lim(n ->infinity) lim(m ->infinity) f (x(n), y(m)) = f (x, y). Dales asked if every function has a point of feeble continuity. Our aim in this short note is to show that (assuming the Continuum Hypothesis) the answer is 'no'. Dales also asked what happens for functions taking only two values: we show that in this case the answer is 'yes'. (C) 2009 Elsevier B.V. All rights reserved.
引用
收藏
页码：2629 / 2631
页数：3
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