I ask this question because in the process of reviewing for my topology comp, I began rereading Alg Topology by Hatcher. In the introduction is the famous Bing's House of Two Rooms. I thought this was an interesting example and began reading about it on the web (procrastinating). Several sites note that Bing's house is contractable (as described in Hatcher) but not collapsablecollapsible. The definition of collapsable collapsible does not appear in any of my topology or alg topology books (Munkres, Hatcher, Spanier) and the only definition I have found is on wikipedia. So this brings me to my question, is collapsable collapsible a useful topological concept? And can anyone show me why Bing's house is not collapsable collapsible (I guess I probably do not fully comprehend the definition)?
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Is the topological concept of collapsable collapsible useful? |
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Is the topological concept of collapsable useful?I ask this question because in the process of reviewing for my topology comp, I began rereading Alg Topology by Hatcher. In the introduction is the famous Bing's House of Two Rooms. I thought this was an interesting example and began reading about it on the web (procrastinating). Several sites note that Bing's house is contractable (as described in Hatcher) but not collapsable. The definition of collapsable does not appear in any of my topology or alg topology books (Munkres, Hatcher, Spanier) and the only definition I have found is on wikipedia. So this brings me to my question, is collapsable a useful topological concept? And can anyone show me why Bing's house is not collapsable (I guess I probably do not fully comprehend the definition)?
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