Bing Playhouse Figure Set. Comes with Bing Bunny & Flop Figures & Foldaway House, From CBeebies TV Show. Tough & Colourful Toddler Toys. Kids Aged 12 Months+.

Product Information

Here is where I could tell you how I saw that the space was contractible, but I’m not going to do that. I think the best way to see it is to make it out of clay or any pliable material you have on hand. Hatcher’s diagram and description give a good recipe, and I know from personal experience that undergraduates and even postdocs like me can follow the instructions well enough to create a convincing house with two rooms, although I must admit our roof was leaky. The house with two rooms is sometimes called Bing’s house after R. H. Bing, the mathematician who first described the space. But like many math students, I first encountered it in Allen Hatcher’s algebraic topology book. He gives us the following picture and definition of the space.

Since 1995, Westwood Bing (a.k.a the five sisters) has actually been a scheduled monument and is now protected for posterity. They’ve become a symbol of West Lothian, and a memorial to the shale oil industry, yet the famous five-leafed bing is an oddity, a one of a kind.

You know how instead of doing a handshake, you could grab each other’s wrists? And your thumbs almost but don’t quite reach your fingers? Bing’s glove for two hands would fit snugly.

This allowed a huge saving of labour, and created a very different shape of mound to the traditional shale bing. Perhaps because the shale was broken to a smaller size and more bound oil was extracted during retorting process, the Westwood bing supports vegetation more readily and have greened much faster than other shale bings. The Sisters remain in private ownership, and access is discouraged. Without hikers boots or swarms of trail bikes they grow a denser cloak of grass and shrub every year. Athletic cattle sometimes find their way up the lower levels of the bing in search of rare and tasty vegetation, but seem to do little damageContractible” is topological shorthand for “like a point” or, not to put too fine a point on it, “boring.” A space is contractible if it you can smush it down to a point without tearing the space or gluing any parts of it together.For example, a solid ball is contractible because even though it is three- rather than zero-dimensional like a point, it can be shrunk down all the way to a point without tearing or collapsing any of its interesting features. Hence, for some topological purposes, it’s close enough to being a point that we might as well assume it is. If your eyes glazed over a bit there, you’re not alone. The picture and description are hard to parse. Before we try to understand the space itself, we should figure out why we would bother with it at all. Hatcher uses it as an example of a space that is “contractible but not in any obvious way.”