it is path-connected and every path between two points can be continuously transformed, staying within the space, into any other path while preserving the two endpoints in question
If the loop can always shrink all the way to a point, then the aquarium's interior is simply connected.
whenever p : [0,1] → X and q : [0,1] → X are two paths (i.e.: continuous maps) with the same start and endpoint (p(0) = q(0) and p(1) = q(1)), then p and q are homotopic relative {0,1}.
Hence the term simply connected: for any two given points in X, there is one and "essentially" only one path connecting them.
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