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Post Closed as "Not suitable for this site" by user44191, Sean Lawton, Yemon Choi, Davide Giraudo, Wojowu
corrected the modality
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Todd Trimble
Todd Trimble
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Let $E$ be a compact metric space. Suppose that closure of every open ball $B(a,r)$ is the closed ball $B'(a,r)$. Can it be thatMust every open ball in $E$ isbe connected.? I think it most probably is. But I don't know how to go about proving this.

Let $E$ be a compact metric space. Suppose that closure of every open ball $B(a,r)$ is the closed ball $B'(a,r)$. Can it be that every open ball in $E$ is connected. I think it most probably is. But I don't know how to go about proving this.

Let $E$ be a compact metric space. Suppose that closure of every open ball $B(a,r)$ is the closed ball $B'(a,r)$. Must every open ball in $E$ be connected? I think it most probably is. But I don't know how to go about proving this.

Added mathmode for math objects.
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edit approved Mar 15, 2019 at 14:51
David Mehrle
edit approved Mar 15, 2019 at 14:51
David Mehrle
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Let E$E$ be a compact metric space. Suppose that closure of every open ball B(a,r)$B(a,r)$ is the closed ball B'(a,r)$B'(a,r)$. Can it be that every open ball in E$E$ is connected. I think it most probably is. But I don't know how to go about proving this.

Let E be a compact metric space. Suppose that closure of every open ball B(a,r) is the closed ball B'(a,r). Can it be that every open ball in E is connected. I think it most probably is. But I don't know how to go about proving this.

Let $E$ be a compact metric space. Suppose that closure of every open ball $B(a,r)$ is the closed ball $B'(a,r)$. Can it be that every open ball in $E$ is connected. I think it most probably is. But I don't know how to go about proving this.

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cherry
cherry
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Requirement for connected sets

Let E be a compact metric space. Suppose that closure of every open ball B(a,r) is the closed ball B'(a,r). Can it be that every open ball in E is connected. I think it most probably is. But I don't know how to go about proving this.