Some topological and combinatorial properties preserved by inverse limits

TL;DR

This paper investigates how certain topological and combinatorial properties such as countable fan-tightness and selective separability are maintained when constructing inverse limits, supported by various examples.

Contribution

It demonstrates the preservation of specific properties under inverse limits and provides illustrative examples based on countable spaces.

Findings

Countable fan-tightness is preserved under inverse limits.

Selective separability is maintained through inverse limits.

Examples illustrate the theoretical results.

Abstract

We show that the following properties are preserved under inverse limits: countable fan-tightness, q+, discrete generation and selective separability. We also present several examples based on inverse limits of countable spaces.