Strongly meager sets and their uniformly continuous images

Strongly meager sets and their uniformly continuous images
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by Andrzej Nowik and Tomasz Weiss PDF

Proc. Amer. Math. Soc. 129 (2001), 265-270 Request permission

We prove the following theorems: (1) Suppose that $f:2^\omega \to 2^\omega$ is a continuous function and $X$ is a Sierpiński set. Then

[(A)] for any strongly measure zero set $Y$, the image $f[X+Y]$ is an $s_0$-set,
[(B)] $f[X]$ is a perfectly meager set in the transitive sense.

(2) Every strongly meager set is completely Ramsey null.

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