Minimal convergence spaces

Kent, D. C.; Richardson, G. D.

doi:10.1090/S0002-9947-1971-0286063-1

Minimal convergence spaces
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by D. C. Kent and G. D. Richardson

Trans. Amer. Math. Soc. 160 (1971), 487-499

DOI: https://doi.org/10.1090/S0002-9947-1971-0286063-1

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Abstract:

We are primarily concerned with minimal ${\text {P}}$ convergence spaces, where ${\text {P}}$ is one of the following convergence space properties: Hausdorff, ${{\text {T}}_2}, \lambda$-regular, $\lambda$-Urysohn, and first countable, $\lambda$ an infinite cardinal number. Our conclusions usually resemble the corresponding topological results, but with some deviations ; for instance, a minimal Hausdorff convergence space is always compact, whereas a countable minimal regular convergence space need not be compact.

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