Abstract
This paper proposes quasi-Cauchy sequences in $\theta$-parametric metric spaces, a generalized metric framework introduced by Moussaoui et al. in 2024. It establishes fundamental relationships among convergent, Cauchy, and quasi-Cauchy sequences, and puts forward concepts of ward compactness and ward continuity in $\theta$-parametric metric spaces. Moreover, the present paper demonstrates that ward continuity on a ward-compact subset in which every quasi-Cauchy sequence admits a convergent subsequence implies ordinary continuity, that uniformly continuous functions are necessarily ward continuous, and that uniform limits of ward-continuous functions preserve ward continuity. Consequently, all ward-continuous functions on $E$ form a closed set of continuous functions on $E$.
References
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Details
| Primary Language | English |
|---|---|
| Subjects | Topology |
| Journal Section | Research Article |
| Authors | |
| Submission Date | December 19, 2025 |
| Acceptance Date | March 5, 2026 |
| Publication Date | March 30, 2026 |
| DOI | https://doi.org/10.53570/jnt.1845528 |
| IZ | https://izlik.org/JA38JU23BP |
| Published in Issue | Year 2026 Issue: 54 |
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