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Consider the topology on $\mathbb{R}^2$ generated by subsets that are open in some line forfrom the origin. ItThis topological space is connected, has the cardinality of continuum, and has $2^c$ open subsets.
Consider the topology on $\mathbb{R}^2$ generated by subsets that are open in some line for the origin. It is connected, cardinality of continuum, and has $2^c$ open subsets.
Consider the topology on $\mathbb{R}^2$ generated by subsets that are open in some line from the origin. This topological space is connected, has the cardinality of continuum, and has $2^c$ open subsets.
Consider the topology on $\mathbb{R}^2$ generated by subsets that are open in some line for the origin. It is connected, cardinality of continuum, and has $2^c$ open subsets.
