On the cardinality of $\pi(\delta)$

Attila Losonczi

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arXiv · 1901.10054

On the cardinality of $\pi(\delta)$

Attila Losonczi

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Abstract

We prove that the cardinality of transitive quasi-uniformities in a quasi-proximity class is at least $2^{2^{\aleph_0}}$ if there exist at least two transitive quasi-uniformities in the class. The transitive elements of $\pi(\delta)$ are characterized if ${\cal V}_{\delta}$ is transitive, and in this case we give a condition when there exists a unique transitive quasi-uniformity in $\pi(\delta)$.

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Attila Losonczi. 2019-01-18. On the cardinality of $\pi(\delta)$. https://arxiv.org/abs/1901.10054

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