Are the things in opposite directions from each other from our point of view at the same distance, moving away from us at the same speed? I heard somewhere, and I really don't recall the source, that red shift seems to indicate that we are in the center if it all. IOW, the red shift of all objects of an equal distance from the earth is the same. Is this correct? I hope you get what I'm asking. I'm not sure how to explain well what I mean.
I understand what you mean, and the last I heard on the subject, estimate are that we are "close" to the center. However, assuming space expands uniformly (i.e. one part doesn't expand more or faster than another part), objects in opposite directions that are equal distances from us would show the same redshift regardless of whether we are at the center of the universe. So, I don't think that redshift is the evidence, but I could be mistaken.
The universe appears to be symmetrical, more or less, with us at the center. That we appear to be at the center is probably an illusion. If it is not an illusion, there are bigger problems with physics and cosmology than we thought.
"Are the things in opposite directions from each other from our point of view at the same distance, moving away from us at the same speed? I heard somewhere, and I really don't recall the source, that red shift seems to indicate that we are in the center if it all. IOW, the red shift of all objects of an equal distance from the earth is the same. Is this correct? I hope you get what I'm asking. I'm not sure how to explain well what I mean."
The universe looks the same to us, out in every direction, as far as we can see. We cannot see to any "edge" nor can an "center" be detected. All galaxies in all directions are receding from all other galaxies, with small exceptions on a local scale.
So we can't even tell if there is a "center" let alone whether we are it. All properties of space appear uniform in all directions