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 [a,b] 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 a circle wrapped twice ? What is confusing me is that any closed interval is homeomorphic to [0,1], so either we have disjoint closed interval, they are homeomophically same. Am I write?
Please guide me and any help is highly appreciated.
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 [a,b] 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 a circle wrapped twice ? What is confusing me is that any closed interval is homeomorphic to [0,1], so either we have disjoint closed interval, they are homeomophically same. Am I write?
Please guide me and any help is highly appreciated.