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edit approved May 1, 2016 at 7:46
Amir Sagiv
edit approved May 1, 2016 at 7:46
Amir Sagiv
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A question about the dispersion points of connected metric spaces.

Let C$C$ be an infinite, separable and connected metric space. If C$C$ becomes totally disconnected disconnected when one of its points p$p\in C$ is removed, does every closed ball of C$C$ with positive radius and center p$p$ always contain an infinite connected subset?

A question about the dispersion points of connected metric spaces.

Let C be an infinite, separable and connected metric space. If C becomes totally disconnected when one of its points p is removed, does every closed ball of C with positive radius and center p always contain an infinite connected subset?

A question about the dispersion points of connected metric spaces

Let $C$ be an infinite, separable and connected metric space. If $C$ becomes totally disconnected when one of its points $p\in C$ is removed, does every closed ball of $C$ with positive radius and center $p$ always contain an infinite connected subset?

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Garabed Gulbenkian
Garabed Gulbenkian
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A question about the dispersion points of connected metric spaces.

Let C be an infinite, separable and connected metric space. If C becomes totally disconnected when one of its points p is removed, does every closed ball of C with positive radius and center p always contain an infinite connected subset?