The topology of 2 circles, unlinked or linked should be the same. One can be transformed into the other only in a higher plane. So we basically have topological invariance, but is there metaphorical invariance?
For Michelangelo’s Sistine Chapel painting, one has, in part, a manifold extending (reaching) out towards another. So would any cardinality change for manifolds, be considered to have topological change if 2 such manifolds become apposed? For the latter example, one would seem to have topological change, especially if respective manifolds had different continua (resultant mixed continua, ‘… rough hewed though it be’ ?), as is usually considered; also metaphorical change? So for comparison of above examples, one seems to have a difference in topological outcome; but metaphorically would the respective outcomes appear the same, although the former is more abstract? TMM
See also: The fly and Little Circle
Am not I
A little circle like thee?
Or art not thou
A larger Circle like me?