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The study aims to characterize the equality of topologies on C_c(X) and explore the implications for spaces denoted as N-spaces.

June 14, 2026Open Access

A NOTE ON Cc(X) VIA A TOPOLOGICAL RING

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This note investigates topological rings C_c(X) and C_c^*(X) with implications for N-spaces.

The study aims to characterize the equality of topologies on C_c(X) and explore the implications for spaces denoted as N-spaces.
Investigated the properties of C_c(X) and C_c^*(X) under m_c and u_c topologies.
Introduced and studied N-spaces and their relation to pseudocompactness.
Established conditions for the coincidence of m_c-topology on C_c(X) with its relative topology in C(X).
Demonstrated that m_c-topology on C_c(X) coincides with its subspace topology if and only if X is an N-space.
Established that X being pseudocompact is equivalent to being countably pseudocompact and an N-space.

MOHAMADİAN et al. (2023) studied this question.

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