If the body is immersed in quintessence, it is under a time stop effect. Can a spirit attempting to "return to its’ body" do so in such circumstances?
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I’m currently studying foliation theory, and to solve a problem I need the following to be true, but I can’t prove nor disprove, I just have a feeling it may be false in general: if I have a smooth manifold $ M,$ and a connected embedded submanifold $ P$ of $ M,$ which is contained in an immersed submanifold $ F$ of $ M,$ is $ P$ also connected in the immersed submanifold topology of $ F$ ?
At first I thought this was obviously true, but giving it a little more thinking, either I’m making some mistake or, if this is true, it is certainly not obvious. Here is what I did: $ F$ may have a finer topology than its subspace topology. If $ F$ was an embedded manifold, then the subspace topology of $ P$ in $ M$ would coincide with its the subspace topology as a subset of $ F,$ and then it would be connected in $ F$ . But with $ F$ being immersed, $ P$ with a topology induced by the immersed topology of $ F$ may have an open set which messes with its connectedness. Any ideas, or did I made some mistake? Thanks.