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Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.

5 votes
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An example of an open discontinuous function

Consider the following simple example of a function $f: \mathbb{R}\to\mathbb{R}$ which is open and discontinuous at all points. If $x\in\mathbb{R}$ is represented as something.$x_1x_2x_3\dots$ in the …