# Maximal monotone normal cones in locally convex spaces

## TL;DR

This paper investigates conditions under which the normal cone in locally convex spaces is maximal monotone, exploring implications like Bishop-Phelps and sum representability results.

## Contribution

It provides new equivalent conditions for maximal monotonicity of normal cones in general locally convex spaces.

## Key findings

- Identifies conditions for maximal monotonicity of normal cones.
- Derives Bishop-Phelps and sum representability results.
- Extends theory to general locally convex spaces.

## Abstract

Equivalent conditions that make the normal cone maximal monotone are investigated in the general settings of locally convex spaces. Some consequences such as Bishop Phelps and sum representability results are presented in the last part.