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+-SH safe2174242 +-SH edit172982 +-SH edited screencap90446 +-SH screencap295719 +-SH twilight sparkle357723 +-SH alicorn314110 +-SH pony1602413 +-SH g42028847 +-SH sparkle's seven1833 +-SH droste effect241 +-SH eye reflection984 +-SH faic14889 +-SH female1802604 +-SH forever232 +-SH fractal103 +-SH narcissism380 +-SH pudding face206 +-SH recursion443 +-SH reflection4677 +-SH smiling397401 +-SH solo1426008 +-SH twilight sparkle (alicorn)149112
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Nice :>
Gaze: P(F) β P(F), Β
where P(F) is the set of all nonempty compact subsets of F.
Β
For any subset S in P(F), Gaze(S) = two smaller copies of S scaled into each eye of Twilight.
Β
Then itβs easy to show that Gaze has a unique fixed point in P(F), homeomorphic to the Cantor set
Β
Proof: By not sure what theorem it is, P(F) is complete under Hausdorff metric. Gaze is a contraction mapping under Hausdorff metric. Then use contraction mapping theorem. For details, see
Β
To show that the fixed point is actually homeomorphic to the Cantor set 2^Ο, explicitly define the homeomorphism in the obvious way.
you know what they all say⦠eyes are the window to the soul
Edited