What question did this study set out to answer?

This research aims to determine the separability properties of the function spaces related to Tychonoff spaces.

For any space X, either Cₚ (X) or CₚCₚ (X) is -separable

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Randomized trial explores properties of function spaces in Tychonoff spaces, indicating relationships between separability and space characteristics.

This research aims to determine the separability properties of the function spaces related to Tychonoff spaces.
Establishes the existence of dense subspaces in function spaces under specific conditions.
Provides examples of spaces exhibiting non-tightness and separability characteristics.
Analyzes compact zero-dimensional spaces and their implications on functional separability.
Demonstrates that at least one of the spaces C_p(X) or C_pC_p(X) is ψ-separable for any Tychonoff space X.
Shows that for certain spaces, C_p(X) lacks a dense subspace of countable functional tightness.
Identifies conditions under which C_p(K) has a dense exponentially separable subspace if K is ω-monolithic.

Aguilar-Velázquez et al. (2026) studied this question.

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Randomized trial explores properties of function spaces in Tychonoff spaces, indicating relationships between separability and space characteristics.