More of my ArXiv papers

[Douglas Bridges]

Dear CN subscribers,

Here are two more papers that I have put on the arXiv recently:

1   Locatedness, Convexity, and Measurability in R^{N}

      https://doi.org/10.48550/arXiv.2607.15558

This paper gives an improved, corrected, Bishop-style constructive development of two theorems originally presented in my paper number [33] --- namely:

Theorem 1. Let S = (S¹,S⁰) be a Lebesgue measurable complemented set in R^{N} with positive (possibly infinite) measure, such that S¹ is convex. Then S¹ is located in R^{N}.

Theorem 2. Let S be a Lebesgue measurable complemented set in R^{N} such that S¹ is convex and has inhabited complement. Then that complement is located in R^{N}.

In particular, where the original proof of Theorem 1 in my paper [33] applied only when S¹ was bounded, the new proof applies without that restriction.

11  Notes on q-normed spaces in constructive analysis

       https://doi.org/10.48550/arXiv.2606.25236

What we call q-normed (linear) spaces were introduced into constructive analysis, under the name pseudonormed spaces, by D.L. Johns, as a means of handling spaces like L_{∞} in which not all elements are constructively normable. We prove a number of q-normed-space analogues/generalisations of standard theorems in the constructive analysis of normed linear spaces, and give examples showing that two natural analogues are essentially nonconstructive.

Best regards,

Douglas