Selection Principles in Mathematics
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Problems from COC 5

1. Problem 1: Find a space which satisfies S_fin(D,D), but not S_fin(D_Omega,D_Omega).
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2. Problem 2: Is it true that if a space has property S_fin(D_Omega,D_Omega), then each finite power has property S_fin(D,D)?
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3. Problem 3: Is it true that if a space satisfies S_fin(D_Omega,D_Omega), then player ONE has no winning strategy in the game G_fin(D_Omega,D_Omega)?
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4. Problem 4 If for space X each element of D_Omega has a countable subset which is in D_Omega, then does each finite power of X have countable cellularity?
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5. Problem 5 Find a space which has property S₁(D,D), but not S₁(D_Omega,D_Omega)
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