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# Article

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Keywords:
function space; topology of uniform convergence; ideal; uniformity; Lindelöf property; pseudouniform ideal; almost pseudo-$\omega$-bounded
Summary:
Given a Tychonoff space $X$, a base $\alpha$ for an ideal on $X$ is called pseudouniform if any sequence of real-valued continuous functions which converges in the topology of uniform convergence on $\alpha$ converges uniformly to the same limit. This paper focuses on pseudouniform bases for ideals with particular emphasis on the ideal of compact subsets and the ideal of all countable subsets of the ground space.
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