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Can you find a subcover for α for (0,2)?

1. Let α:={...}. Is this an open cover for (0,2)? Can you find a subcover for α for (0,2)?

2. Find an open cover for (0,2) which consists of open balls of the form B1(z) with radius 1, which does not contain any finite subcover.

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This solution is comprised of a detailed explanation of the open cover.
It contains step-by-step explanation for the following problem:
1. Let α:={...}. Is this an open cover for (0,2)? Can you find a subcover for α for (0,2)?

2. Find an open cover for (0,2) which consists of open balls of the form B1(z) with radius 1, which does not
contain any finite subcover.

Solution contains detailed step-by-step explanation.

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