B Special relativity implies the space cannot be "closed"?

[Herman Trivilino]

This occurred to me, while reading, (with almost no understanding) the thread. http://www.businessinsider.com/do-astronauts-age-slower-than-people-on-earth-2015-8 Which explains(?) the gravity time-dilation and the velocity time-Dilation, in uncertain terms.

Well, time dilation due to velocity has nothing to do with the curvature of spacetime, so that is a misconception. One that's probably not relevant to this discussion. But the fact that time dilation is symmetrical is something they ignore in that article, and that is relevant. They state that astronaut Scott Kelly aged 0.01 seconds less than his brother Mark Kelly who stayed on Earth because Scott was moving at a speed of 5 mi/h. Mark is moving at 5 mi/h relative to Scott, and the author of the article doesn't explain why that doesn't make Mark the one who is younger. This is the part that's relevant to this discussion: Scott is the one who takes the shorter path through spacetime, and that is the reason he ages less.

In this, and other, explanations, the 'traveler' must accelerate, to return to the original location.

And that is the misconception that underlies the OP's original query: The traveler takes the shorter path through spacetime to get to the reunion. Whether that happens because of acceleration or not.