Nbd is not cartesian closed

TL;DR

This paper demonstrates that the category of neighborhood spaces does not possess the property of being cartesian closed, highlighting a fundamental limitation in its categorical structure.

Contribution

It provides a concise proof that neighborhood spaces do not form a cartesian closed category, clarifying their categorical properties.

Findings

Neighborhood spaces are not cartesian closed.

The result impacts the understanding of categorical structures in topology.

The paper clarifies limitations in neighborhood space categories.

Abstract

In this short note it is shown that the category of neighborhood spaces is not cartesian closed.