(a) To check: If the given set forms a basis for a topology.

Question

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Answer 1

Question

Chapter 4.36, Problem 5E

To determine

(a)

To check:

If the given set forms a basis for a topology.

To determine

(b)

To show:

Each of the spaces X−{p} and X−{q} is homeomorphic to ℝ.

To determine

(c)

To show:

The space X satisfies the T1 axiom, but is not Hausdorff.

To determine

(d)

To show:

The space X satisfies all the conditions for a 1-manifold except for the Hausdorff condition.

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1. Given that h(t) = -5t + 3 t². A tangent line H to the function h(t) passes through the point (-7, B). a. Determine the value of ẞ. b. Derive an expression to represent the gradient of the tangent line H that is passing through the point (-7. B). c. Hence, derive the straight-line equation of the tangent line H 2. The function p(q) has factors of (q − 3) (2q + 5) (q) for the interval -3≤ q≤ 4. a. Derive an expression for the function p(q). b. Determine the stationary point(s) of the function p(q) c. Classify the stationary point(s) from part b. above. d. Identify the local maximum of the function p(q). e. Identify the global minimum for the function p(q). 3. Given that m(q) = -3e-24-169 +9 (-39-7)(-In (30-755 a. State all the possible rules that should be used to differentiate the function m(q). Next to the rule that has been stated, write the expression(s) of the function m(q) for which that rule will be applied. b. Determine the derivative of m(q)

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Answer 2

Question

Chapter 4.36, Problem 5E

To determine

(a)

To check:

If the given set forms a basis for a topology.

To determine

(b)

To show:

Each of the spaces X−{p} and X−{q} is homeomorphic to ℝ.

To determine

(c)

To show:

The space X satisfies the T1 axiom, but is not Hausdorff.

To determine

(d)

To show:

The space X satisfies all the conditions for a 1-manifold except for the Hausdorff condition.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 4.36, Problem 5E

To determine

(a)

To check:

If the given set forms a basis for a topology.

To determine

(b)

To show:

Each of the spaces X−{p} and X−{q} is homeomorphic to ℝ.

To determine

(c)

To show:

The space X satisfies the T1 axiom, but is not Hausdorff.

To determine

(d)

To show:

The space X satisfies all the conditions for a 1-manifold except for the Hausdorff condition.

Expert Solution & Answer

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See solution

Answer 4

Question

Chapter 4.36, Problem 5E

To determine

(a)

To check:

If the given set forms a basis for a topology.

To determine

(b)

To show:

Each of the spaces X−{p} and X−{q} is homeomorphic to ℝ.

To determine

(c)

To show:

The space X satisfies the T1 axiom, but is not Hausdorff.

To determine

(d)

To show:

The space X satisfies all the conditions for a 1-manifold except for the Hausdorff condition.

Expert Solution & Answer

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See solution

Answer 5

Chapter 4.36, Problem 5E

To determine

(a)

To check:

If the given set forms a basis for a topology.

To determine

(b)

To show:

Each of the spaces X−{p} and X−{q} is homeomorphic to ℝ.

To determine

(c)

To show:

The space X satisfies the T1 axiom, but is not Hausdorff.

To determine

(d)

To show:

The space X satisfies all the conditions for a 1-manifold except for the Hausdorff condition.

Answer 6

Chapter 4.36, Problem 5E

To determine

(a)

To check:

If the given set forms a basis for a topology.

Answer 7

Chapter 4.36, Problem 5E

To determine

(a)

To check:

If the given set forms a basis for a topology.

Answer 8

To determine

(b)

To show:

Each of the spaces X−{p} and X−{q} is homeomorphic to ℝ.

Answer 9

To determine

(b)

To show:

Each of the spaces X−{p} and X−{q} is homeomorphic to ℝ.

Answer 10

To determine

(c)

To show:

The space X satisfies the T1 axiom, but is not Hausdorff.

Answer 11

To determine

(c)

To show:

The space X satisfies the T1 axiom, but is not Hausdorff.

Answer 12

To determine

(d)

To show:

The space X satisfies all the conditions for a 1-manifold except for the Hausdorff condition.

Answer 13

To determine

(d)

To show:

The space X satisfies all the conditions for a 1-manifold except for the Hausdorff condition.

Answer 14

Expert Solution & Answer

Answer 15

Expert Solution & Answer

Answer 16

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Answer 17

Ch. 4.30 - Show that l and I02 are not metrizable.Ch. 4.30 - Which of our four countability axioms does S...Ch. 4.30 - Which of our four countability axioms does in the...Ch. 4.30 - Let A be a closed subspace of X. Show that if X is...Ch. 4.30 - Prob. 10E Ch. 4.30 - Let f:XY be continuous. Show that if X is...Ch. 4.30 - Let f:XY be continuous open map. Show that if X...Ch. 4.30 - Show that if X has a countable dense subset, every...Ch. 4.30 - Show that if X is Lindelof and Y is compact, then...Ch. 4.30 - Give I the uniform metric, where I=[0,1]. Let...

(a) To check: If the given set forms a basis for a topology.

Solution Summary: The author explains how X forms a basis for the topology as shown below. The set is given by R-left0rightcup

Concept explainers

(a)

To check:

If the given set forms a basis for a topology.

(b)

To show:

Each of the spaces X−{p} and X−{q} is homeomorphic to ℝ.

(c)

To show:

The space X satisfies the T1 axiom, but is not Hausdorff.

(d)

To show:

The space X satisfies all the conditions for a 1-manifold except for the Hausdorff condition.

Want to see the full answer?

Chapter 4 Solutions

(a) To check: If the given set forms a basis for a topology.

Solution Summary: The author explains how X forms a basis for the topology as shown below. The set is given by R-left0rightcup

Concept explainers

(a) To check: If the given set forms a basis for a topology.

(b) To show: Each of the spaces X−{p} and X−{q} is homeomorphic to ℝ.

(c) To show: The space X satisfies the T1 axiom, but is not Hausdorff.

(d) To show: The space X satisfies all the conditions for a 1-manifold except for the Hausdorff condition.

Want to see the full answer?

Chapter 4 Solutions

(a)

To check:

If the given set forms a basis for a topology.

(b)

To show:

Each of the spaces X−{p} and X−{q} is homeomorphic to ℝ.

(c)

To show:

The space X satisfies the T1 axiom, but is not Hausdorff.

(d)

To show:

The space X satisfies all the conditions for a 1-manifold except for the Hausdorff condition.