Continuous images of sets of reals

doi:10.1016/S0166-8641(00)00079-1

Topology and its Applications

Volume 116, Issue 2, 15 November 2001, Pages 243-253

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Abstract

We will show that, consistently, every uncountable set can be continuously mapped onto a non measure zero set, while there exists an uncountable set whose all continuous images into a Polish space are meager.

MSC

03E17

Keywords

Small sets

Measure

Consistency

Cited by (0)

¹: Web page: http://math.idbsu.edu/~tomek. The first author was partially supported by NSF grant DMS 9971282.

²: Web page: http://math.rutgers.edu/~shelah/. The second author was partially supported by Israel Science Foundation. Publication 722.