embedding of of two closed intervals in R^3 give embeddding of circle wrapped twice??

Dear all; I am wondering if we can glue two closed intervals to form a circle wrapped twice. I mean if we have tow disjoint closed intervals [0,1] and join the end point of the first interval to the start point of the second, and joining the end point of the second to the start point of the first, what we will get? I am confusing. I think that we can get a circle or may be an embedding of circle wrapped twice ? Suppose this construction is in R^3, then is it embedding of a circle or a circle wrapped twice? What do you think? Please help me and any guidance or comment is highly appreciated Best Regards;

Re: embedding of of two closed intervals in R^3 give embeddding of circle wrapped twi

what is confusing me is that any closed interval is homeomorphic to [0,1]. So, even we have disjoint closed intervals, they are homeomorphically same.

Please guide me