Bing's House and homotopies

Muestra que si f es la función que encaja a $S^{1}$ en la circunferencia que rodea al cilindro mayor, por la mitad, de la casa de Bing, entonces f es homotópica a una constante.

Show that if $\,f\,$ is the function embedding $\,S^1\,$ in the circumference around the main cylinder, at its half, of Bing's House, then $\,f\,$ is homotopic to a constant.

Here is the description of this space from page 4 of Hatcher's Algebraic Topology:

• ¿quien es Bing? Apr 21, 2013 at 2:29
• Sería una buena idea que pusieras algo de trabajo propio que hayas hecho en esto. Yo no tengo ni idea, pero preguntas que no muestran un poco de esfuerzo hecho no son bien recibidas aquí muchas veces. Apr 21, 2013 at 2:30
• @EricO.Korman, Chandler Bing, from "Friends"...:) Seriously: this seems to be a rather weird (for me) topological construction of something contractible but that looks...well, like a weird house.I never heard of it before. Apr 21, 2013 at 2:32
• @DonAntonio so this question is asking about the inclusion of $S^1$ in a cone? Apr 21, 2013 at 2:41
• No, Bing's House is the construction called "The House with Two Rooms" in Hatcher. This is relevant. Apr 21, 2013 at 2:42