The paper is devoted to the investigation of topological properties of space mappings. It is shown that orientation-preserving mappings f W D ! R n in a domain D R n ; n 2; which are more general than mappings with bounded distortion, are open and discrete if a function Q corresponding to the control of the distortion of families of curves under these mappings has slow growth in the domain f .D/; e.g., if Q has finite mean oscillation at an arbitrary point y 0 2 f .D/: