# Characterizations of topological manifolds modeled on absorbing sets in non-separable Hilbert spaces and the discrete cells property

## TL;DR

This paper characterizes infinite-dimensional manifolds in non-separable Hilbert spaces using the discrete cells property and explores related approximation properties, advancing understanding of their topological structure.

## Contribution

It introduces new characterizations of manifolds modeled on absorbing sets in non-separable Hilbert spaces via the discrete cells property and extends the discrete approximation property.

## Key findings

- Characterization of manifolds using the discrete cells property
- Extension of the discrete (locally finite) approximation property
- Deeper understanding of topological structures in infinite-dimensional spaces

## Abstract

In this paper, we characterize infinite-dimensional manifolds modeled on absorbing sets in non-separable Hilbert spaces by using the discrete cells property, which is a general position property. Moreover, we study the discrete (locally finite) approximation property, which is an extension of the discrete cells property.