1. For each of the following spaces, determine (if you can) which of these properties it satisfies. (Assume the Tychonoff theorem if you need it.) (a) So (b) Sa (c) S× S (d) The ordered square (e) Re (f) R² (g) R in the product topology (h) R in the uniform topology (i) R in the box topology (j) R¹ in the product topology, where I = [0, 1] (k) RK
1. For each of the following spaces, determine (if you can) which of these properties it satisfies. (Assume the Tychonoff theorem if you need it.) (a) So (b) Sa (c) S× S (d) The ordered square (e) Re (f) R² (g) R in the product topology (h) R in the uniform topology (i) R in the box topology (j) R¹ in the product topology, where I = [0, 1] (k) RK
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![1. For each of the following spaces, determine (if you can) which of these properties
it satisfies. (Assume the Tychonoff theorem if you need it.)
(a) So
(b) Sa
(c) S× S
(d) The ordered square
(e) Re
(f) R²
(g) R in the product topology
(h) R in the uniform topology
(i) R in the box topology
(j) R¹ in the product topology, where I = [0, 1]
(k) RK](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feabade52-5174-4cc3-8205-365538407c90%2Fbb5eff21-d1c7-4123-b468-9e9ada3ad2c9%2Fp91241_processed.png&w=3840&q=75)
Transcribed Image Text:1. For each of the following spaces, determine (if you can) which of these properties
it satisfies. (Assume the Tychonoff theorem if you need it.)
(a) So
(b) Sa
(c) S× S
(d) The ordered square
(e) Re
(f) R²
(g) R in the product topology
(h) R in the uniform topology
(i) R in the box topology
(j) R¹ in the product topology, where I = [0, 1]
(k) RK
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