  We give two examples of metric measure spaces satisfying the measure
contraction property MCP(K,N) but having different topological dimensions at
different regions of the space. The first one satisfies MCP(0,3) and contains a
subset isometric to $\mathbb{R}$, but does not topologically split. The second
space satisfies MCP(2,3) and has diameter $\pi$, which is the maximal possible
diameter for a space satisfying MCP(N-1,N), but is not a topological spherical
suspension. The latter example gives an answer to a question by Ohta.
