# Strongly sequentially separable function spaces, via selection principles

## TL;DR

This paper investigates strongly sequentially separable function spaces, particularly spaces of continuous and Borel functions on Tychonoff spaces, providing solutions to an open problem in the field.

## Contribution

It introduces new results characterizing strongly sequentially separable function spaces and resolves a previously posed open problem by Gartside, Lo, and Marsh.

## Key findings

- Characterization of strongly sequentially separable function spaces
- Resolution of an open problem in the literature
- Analysis of properties of function spaces with pointwise convergence topology

## Abstract

A separable space is strongly sequentially separable if, for each countable dense set, every point in the space is a limit of a sequence from the dense set. We consider this and related properties, for the spaces of continous and Borel real-valued functions on Tychonoff spaces, with the topology of pointwise convergence. Our results solve a problem stated by Gartside, Lo, and Marsh.