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Francesco Polizzi
Francesco Polizzi
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QUESTION: My question is the following:

Does there exist a connected metric space $\ X,\ $ where $\ |X|>1,\ $ such that there does not exist any separable connected subspace $\ Y,\ $ with $\ |Y|>1\ $?

Does there exist a connected metric space $\ X,\ $ where $\ |X|>1,\ $ which contains no separable connected subspace $\ Y\ $ with $\ |Y|>1\ $?

QUESTION:

Does there exist a connected metric space $\ X,\ $ where $\ |X|>1,\ $ such that there does not exist any separable connected subspace $\ Y,\ $ with $\ |Y|>1\ $?

My question is the following:

Does there exist a connected metric space $\ X,\ $ where $\ |X|>1,\ $ which contains no separable connected subspace $\ Y\ $ with $\ |Y|>1\ $?

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Włodzimierz Holsztyński
Włodzimierz Holsztyński
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Connected metric spaces without connected separable subspaces

QUESTION:

Does there exist a connected metric space $\ X,\ $ where $\ |X|>1,\ $ such that there does not exist any separable connected subspace $\ Y,\ $ with $\ |Y|>1\ $?