On page 4 of Hatcher's "Algebraic Topology" he constructs the "house with two rooms" space. He claims that there is some neighborhood containing this space that is homeomorphic to the unit ball (in $\mathbb{R}^3$). I was hoping someone would demonstrate how to prove this.
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3You might appreciate this blog post with lots of great pictures. – Feb 23 '15 at 09:12
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I had referred to the website Mike cited when I was taking topology. You can literally draw step by step sketches to obtain a ball. Collect the rooms to their respective entries and then pull their boundaries out (via their entries). Or you are looking for a more rigorous proof perhaps? – Alp Uzman Feb 23 '15 at 09:23