As I don´t think time has any properties I disagree. First, AFAIK "topology" is concerned only with shape and really just the connectivity of it not the sizes. (People and donuts have same doublely connected shape to a topologist.)
I'm specifically referring to the notion of a topological space, which is the basis for e.g. differential geometry. Time is universally modelled as a differentiable manifold or at least as part of one in physics, which among other things means it has topology associated with it.
Secondly, as I think you know from your later mention of the mixing of time and space coordinates when describing how events in one frame would be described in another frame, there is no special aspect of "simultanity" as you seem to assert.
There is, in spacetime, in the sense that physical interactions have a property of locality with respect to space and time. In e.g. Lagrange formulations of physical theories, the behaviour of particles and fields are always coupled to other particles or fields at the same place and time.
But what I was mainly referring to is something you wrote earlier, which is this idea that, at least sometimes, you can eliminate the t variable from the description of an evolving physical system (I think you used the example of two planets orbiting one another). But even if you do that, you're still left with an equation stating that certain positions of one planet are "associated" with different positions of another planet, which is essentially expressing an underlying concept of simultaneity, or distinct "time frames", or whatever you might want to call it.
Many things are the same in all frames. E.g. The topology of an object is the same for all frames and H2O freezes at 0 C in all, but lengths and time intervals say between two LED flashes, measure by local clocks also change (don´t agree) and can be simultaneous in only one frame. These difference are just in how one frame describes meter sticks and light flashes, of another frame, not real changes in one frame.
You've misunderstood what I said. Actually much of what you're saying here is exactly the point I'm making. According to special relativity, there is a symmetry in physics which means that there are a whole bunch of different time and distance measurement standards, related to each other by Lorentz or more generally Poincaré transformations, that are all "equally good" as one another, in the sense that the laws of physics take the same form in all of them and none of them have any special measurable properties. Because one reference frame's space and time coordinates are actually a mixture of other frame's space and time coordinates, I don't see how you could claim that time doesn't fundamentally exist while space does without breaking relativity at least in spirit. Suppose space exists and I parameterise it with an $$x$$ coordinate, and suppose time doesn't fundamentally exist but somehow emerges as a useful parameter which I call $$t$$. Then what the hell are $$x' \,=\, \gamma(x \,-\, vt)$$ and $$t' \,=\, \gamma(t \,-\, \frac{v}{c^{2}} x)$$?
Incidentally, regarding what you say in post #78, in general relativity it's the spacetime manifold, and not just space, that can curve.
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