✦ LIBER ✦

Sequential, pointwise, and uniform continuity: A constructive note

✍ Scribed by Douglas S. Bridges

Book ID: 102486519
Publisher: John Wiley and Sons
Year: 1993
Tongue: English
Weight: 412 KB
Volume: 39
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.19930390108

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

The main result of this paper is a weak constructive version of the uniform continuity theorem for pointwise continuous, real‐valued functions on a convex subset of a normed linear space. Recursive examples are given to show that the hypotheses of this theorem are necessary. The remainder of the paper discusses conditions which ensure that a sequentially continuous function is continuous. MSC: 03F60, 26E40, 46S30.

📜 SIMILAR VOLUMES

Sequential Continuity of Functions in Co

Sequential Continuity of Functions in Constructive Analysis

✍ Douglas Bridges; Ayan Mahalanobis 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 174 KB 👁 2 views

A short note about pointwise divergence

A short note about pointwise divergence of Jacobi expansion for continuous functions

✍ W. Richter 📂 Article 📅 1982 🏛 Akadmiai Kiad 🌐 English ⚖ 71 KB

Pointwise and uniform convergence on a C

Pointwise and uniform convergence on a Corson compact space

✍ Gabriel Debs 📂 Article 📅 1986 🏛 Elsevier Science 🌐 English ⚖ 294 KB

A note on constructive methods for ramse

A note on constructive methods for ramsey numbers

✍ F. R. K. Chung 📂 Article 📅 1981 🏛 John Wiley and Sons 🌐 English ⚖ 227 KB 👁 1 views

## Abstract Let __r(k__) denote the least integer __n__‐such that for any graph __G__ on __n__ vertices either __G__ or its complement G contains a complete graph __K__~k~ on __k__ vertices. in this paper, we prove the following lower bound for the Ramsey number __r(k__) by explicit construction: _

Apartness, Topology, and Uniformity: a C

Apartness, Topology, and Uniformity: a Constructive View

✍ Douglas Bridges; Peter Schuster; Luminiţa Vîţă 📂 Article 📅 2002 🏛 John Wiley and Sons 🌐 English ⚖ 188 KB

The theory of apartness spaces, and their relation to topological spaces (in the point-set case) and uniform spaces (in the set-set case), is sketched. New notions of local decomposability and regularity are investigated, and the latter is used to produce an example of a classically metrisable apart

A note on construction of nearly uniform

A note on construction of nearly uniform designs with large number of runs

✍ Kai-Tai Fang; Hong Qin 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 134 KB

Uniform designs have been used in computer experiments (Fang et al., Technometrics 42 (2000) 237). A uniform design seeks its design points to be uniformly scattered on the experimental domain. When the number of runs is large, to search a related uniform design is a NP hard problem. Therefore, the