On separable nets in constructive topological spaces

TL;DR

This paper characterizes a class of nets in constructive topological spaces where convergence aligns with subsequence convergence, and derives a corollary related to Riemann integrability in constructive analysis.

Contribution

It introduces a specific class of nets in constructive topological spaces and connects their convergence properties to a theorem on Riemann integrability variants.

Findings

Identified a class of nets with convergence equivalent to subsequence convergence.

Derived a corollary linking strong and weak constructive Riemann integrability.

Established foundational results in constructive topology and analysis.

Abstract

A class of nets in constructive (in A.A.Markov's sense) topological space for which the convergence is equivalent to convergence of all subsequences, is described. B.A.Kushner's theorem about coincidence of strong and weak constructive variants of Riemann's integrability, is obtained as corollary.