The Co-e-filters among C^* (X)
DOI:
https://doi.org/10.51699/cajmtcs.v7i4.976Keywords:
Co-e-filter, ϵ-set, prime z-ϵ-ideal, Co-e-ultrafilter, C^* (X)Abstract
Here we investigate the Co-ϵ-filter sometimes we say Co-e-filter (filters of Cozero e-set) and e-ideal association of C^* (X) for real-valued bounded continuous functions on Tychonoff space X, the essential concept of the study is Coz-filters of bounded continuous functions herein denoted by Co-e-filters for non-compact spaces. We establish the relationship among Co-ϵ-ultrafilters and the minimal prime ideals of C^* (X) providing a direct analogue to the known relationship between e-ultrafilters and maximal ideals, the central result demonstrates a precise correspondence between these co-e-ultrafilters and the minimal prime z-e-ideals of C^* (X), thereby mirroring the established association in C(X) within the bounded context.
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