Negative dimension in general and asymptotic topology

TL;DR

This paper introduces the concept of negative topological dimension and weight for asymptotic topology, applying quantization of negative-dimensional spaces to linguistic statistics.

Contribution

It presents novel definitions of negative topological dimension and asymptotic weight, expanding topological theory and its applications to linguistics.

Findings

Definition of negative topological dimension

Introduction of weight for asymptotic topological dimension

Application to linguistic statistical analysis

Abstract

We introduce the notion of negative topological dimension and the notion of weight for the asymptotic topological dimension. Quantizing of spaces of negative dimension is applied to linguistic statistics.