In each of the following cases, describe or draw a picture of the resulting quotient space. Assume that points are identified only with themselves unless they are explicitly said to be identified with...

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In each of the following cases, describe or draw a picture of the resulting quotient space. Assume that points are identified only with themselves unless they are explicitly said to be identified with...

In each of the following cases, describe or draw a picture of the resulting quotient space. Assume that points are identified only with themselves unless they are explicitly said to be identified with other points.

(a) The disk with its boundary points identified with each other to form a single point.

(b) The circle S1 with each pair of antipodal points identified with each other.

(c) The interval [0, 4], as a subspace of R, with integer points identified with each other.

(d) The interval [0, 9], as a subspace of R, with even integer points identified with each other to form a point and with odd integer points identified with each other to form a different point.

(e) The real line R with [—1, 1] collapsed to a point.

(f) The real line R with [—2, —1] U [1, 2] collapsed to a point.

(g) The real line R with (—1, 1) collapsed to a point.

(h) The plane R2 with the circle S1 collapsed to a point.

(i) The plane R2 with the circle S1 and the origin collapsed to a point.

(j) The sphere with the north and south pole identified with each other.

(k) The sphere with the equator collapsed to a point.

math Advanced-Math

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In each of the following cases, describe or draw a picture of the resulting quotient space. Assume that points are identified only with themselves unless they are explicitly said to be identified with...