Abstract:Given a Tychonoff space $X$, a base $\alpha$ for an ideal on $X$ is called {\it 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.
Keywords: function space; topology of uniform convergence; ideal; uniformity; Lindel\"of property; pseudouniform ideal; almost pseudo-$\omega$-bounded
AMS Subject Classification: 54A10 54A20 54A25 54C35 54D20 54E15