What is this quotient space of the torus?

Let’s learn what is this quotient space of the torus. The most accurate or helpful solution is served by Mathematics.

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Quotient space of the torus with two points identified

Take the torus $T=S_1 \times S_1$. Choose two points $x,y \in T$ and define a quotient topology by identifying $x$ and $y$. Let $X$ denote the quotient space. Prove that: a) Compute the fundamental group of $X$. b) Prove that $X$ is not homeomorphic to a surface.

Answer:

So for part a. Let $T:=S_1 \times S_1$ be the torus. Suppose that $x,y \in T$ such that $x \neq y$ and...

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TJIF at Mathematics Mark as irrelevant Undo

Other solutions

What are the advantages\disadvantages of a sphere, cylinder, torus and dumbell space settlement?

pppppplllllllllllllllllllllllllsssssssss… help me. ihav space settlement competetion. i wud like to know the pros and cons of these shapes

Answer:

You can't create a stable artificial gravity with any of them.Their lack of flat surfaces prevent walking...

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kirthi t at Yahoo! Answers Mark as irrelevant Undo

If spending time in microgravity is detrimental to human bone, why didn't the ISS get designed as a torus a la 2001 A Space Odyssey which then allows for the creation of artificial gravity?

Several science fiction movies show "doughnut" shaped space stations rotating about the axis of the "hole" thus providing artificial gravity via centrifugal force.

Answer:

The main answers are suitability to mission, cost and safety.  As viewed in the film, the 2001 torus...

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Lawrence D. Roberts at Quora Mark as irrelevant Undo

Would helicopters work the same way on a space torus with centrifugal force as they would on a planet with gravity?

In the 2013 film Elysium, which takes place on a orbiting space habitat  that uses centrifugal force to imitate gravity has a great number of scenes showing helicopters. Does it work the same way?

Answer:

Helicopters would fly easier in a Torus as they wouldn't be spinning with the ground, they would have...

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Paul Smith at Quora Mark as irrelevant Undo

Who discovered that the Earth was not shaped like a torus (doughnut)?

Eratosthenes' measurements (and many other astronomical measurements) are consistent with a torus-shaped Earth, on which the Mediterranean is on the outer half of the torus. So is Magellan's circumnavigation. I can think of a few approaches to disproving...

Answer:

Aint you're forgetting gravity? On a torus the gravity would not be always perpendicular to the surface...

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Dick Swart at Quora Mark as irrelevant Undo

There is a torus shaped ring around a planet which gradually condenses to a planar ring (cont)?

Does the ring move: a. towards the planet b. away from the planet c. stays in the same relative position to the planet d. I should have asked the question in the Physics section PS. A torus is a big donut shape of debris: http://groups.csail.mit.edu...

Answer:

I would have to say that it moves towards the planet. Planetary rings become planar due to inelastic...

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Frst Grade Rocks! Ω at Yahoo! Answers Mark as irrelevant Undo

Answer:

Yes. Even if space were toroidal, gravity would pull large masses into aproximately spherical shapes...

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community wiki at wiki.answers.com Mark as irrelevant Undo

Answer:

I do not know what an open space is in Handball. maybe get through the open space? Or the ball goes...

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ChaCha Mark as irrelevant Undo

Answer:

Constructing quotient spaces is a two step procedure: 1) partition the set of points. Each element of...

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Till Plewe at Quora Mark as irrelevant Undo

A few of my many questions about dark, super-dense objects in space.?

I'm a teacher, but not in science. I purposely am not using the term "black hole" because it is too restrictive for the purpose of this question. As I have not taken astronomy or physics, and have no experts to talk with, I have qualms abour...

Answer:

1..Gravity at the poles is equal because the poles are equidistant from the center, the equator is farther...

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John (Thurb) McVey at Yahoo! Answers Mark as irrelevant Undo

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