Ideals of Functions with Compact Support in the Integer-valued Case

Authors

Themba Dube, University of South Africa
Oghenetega Ighedo, Chapman UniversityFollow
Batsile Tlharesakgosi, University of South Africa

Document Type

Article

Publication Date

12-4-2022

Abstract

For a zero-dimensional Hausdorff space X, denote, as usual, by C(X, ℤ) the ring of continuous integer-valued functions on X. If f ∈ C(X, ℤ), denote by Z(f) the set of all points of X that are mapped to 0 by f. The set C_K(X; ℤ) = {f ∈ C(X; ℤ) | cl_X(X \ Z(f)) is compact} is the integer-valued analogue of the ideal of functions with compact support in C(X). By first working in the category of locales and then interpreting the results in spaces, we characterize this ideal in several ways. Writing ζ X for the Banaschewski compactification of X, we also explore some properties of ideals of C(X, ℤ) associated with subspaces of ζ X analogously to how one associates, for any Tychonoff space Y, subsets of β Y with ideals of C(Y).

Comments

This article was originally published in Mathematica Slovaca, volume 72, in 2022. https://doi.org/10.1515/ms-2022-0097

Recommended Citation

T. Dube, O. Ighedo & B. Tlharesakgosi: Ideals of functions with compact support in the integervalued case. Math. Slovaca, 72 (2022) No. 6, 1429 - 1446. https://doi.org/10.1515/ms-2022-0097

Peer Reviewed

1

Copyright

De Gruyter