𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A constructive theory of point-set nearness

✍ Scribed by L.S. Vı̂ţă; D.S. Bridges

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
264 KB
Volume
305
Category
Article
ISSN
0304-3975

No coin nor oath required. For personal study only.

✦ Synopsis

An axiomatic constructive development of the theory of nearness and apartness of a point and a set is introduced as a setting for topology.

📜 SIMILAR VOLUMES

Functional interpretation of Aczel's con
Functional interpretation of Aczel's constructive set theory
✍ Wolfgang Burr 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 266 KB

In the present paper we give a functional interpretation of Aczel's constructive set theories CZF -and CZF in systems T∈ and T + ∈ of constructive set functionals of ÿnite types. This interpretation is obtained by a translation × , a reÿnement of the ∧ -translation introduced by Diller and Nahm (Arc

A note on Bar Induction in Constructive
A note on Bar Induction in Constructive Set Theory
✍ Michael Rathjen 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 113 KB 👁 1 views

## Abstract Bar Induction occupies a central place in Brouwerian mathematics. This note is concerned with the strength of Bar Induction on the basis of Constructive Zermelo‐Fraenkel Set Theory, CZF. It is shown that CZF augmented by decidable Bar Induction proves the 1‐consistency of CZF. This answ

On some peculiar aspects of the construc
On some peculiar aspects of the constructive theory of point-free spaces
✍ Giovanni Curi 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 162 KB

## Abstract This paper presents several independence results concerning the topos‐valid and the intuitionistic (generalised) predicative theory of locales. In particular, certain consequences of the consistency of a general form of Troelstra's uniformity principle with constructive set theory and t