# Some classes of subsemimodule spaces

## TL;DR

This paper investigates the topological properties of certain classes of subsemimodule spaces, revealing conditions for compactness, irreducibility, and disconnectedness, and analyzing continuous maps between these spaces.

## Contribution

It introduces new characterizations of subsemimodule spaces, including conditions for compactness, irreducibility, and disconnectedness, and explores continuous mappings in this context.

## Key findings

- Subsemimodule spaces are $T_0$.
- Finitely generated subsemimodule spaces are compact.
- Conditions for irreducibility and disconnectedness are established.

## Abstract

The aim of this paper is to study the topological properties of some classes of subsemimodules endowed with a subbasis closed-set topology. We show that such spaces are $T_0$. When the semimodule is finitely generated, those spaces are compact as well. We characterize subsemimodule spaces for which every nonempty irreducible closed set has a unique generic point. We give a sufficient condition for a connected subsemimodule space, and using the notion of strongly disconnectedness, we determine compact disconnected subsemimodule spaces. Finally, we discuss continuous maps between subsemimodule spaces.