Versions of Eberlein-\v{S}mulian and Amir-Lindenstrauss theorems in the framework of conditional sets

TL;DR

This paper extends classical theorems in functional analysis to the framework of conditional set theory, providing new conditional versions of key theorems like Eberlein-Mulian and Amir-Lindenstrauss, along with foundational results.

Contribution

It introduces and proves conditional versions of fundamental theorems in weak topology, expanding the scope of these results within the framework of conditional set theory.

Findings

Conditional versions of Eberlein-Mulian Theorem

Conditional versions of Amir-Lindenstrauss Theorem

Conditional Baire Category and Uniform Boundedness Principles

Abstract

Based on conditional set theory, we study conditional weak topologies, extending some well-known results to this framework and culminating with the proof of conditional versions of Eberlein-\v{S}mulian and Amir-Lindenstrauss Theorems. In pursuing this aim, we prove conditional versions of Baire Category Theorem and Uniform Boundedness Principle.