Questions tagged [alexandroff-double-circle]
For questions about the Alexandroff double circle, also called "Concentric Circles" in Steen & Seebach's "Counterexamples in Topology".
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Find the centre of the circle
So there is a square of 50cm length. There are 3 circle's whose centre's are any 3 vertices of the square.The radius(r1,r2,r3) of these circles can be assumed i.e it is known.
Now a 4th circle exists ...
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Example of $f$, $g$ and $a$, such that $(f \circ g)'(a)$ exists, and $g'(a)$ exists, but $f'(g(a))$ does not.
Find an example of 2 functions $f$ and $g$ and a point $a \in
\mathbb{R}$, such that $(f \circ g)'(a)$ and $g'(a)$ exists, but $f'(g(a))$ does not exist, and also $f$ and $g$ must take on all values ...
user838035
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My proof that the Alexandroff double circle not second-countable
I'm hoping someone can comment on if my logic on the Alexandroff double cirlce not being second countable is right.
The Alexandroff double circle has underlying set $C = C_1 \cup C_2$ where $C_i = \{ ...
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Is the Alexandroff double circle separable?
Is the Alexandroff double circle separable (i.e. has a countable dense subset)?
The Alexandroff double circle is the space with underlying set $C = C_1 \cup C_2$, where $C_i$ is the circle of radius $...
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Is the Alexandroff Double Circle first-countable?
The Alexandroff Double Circle is the topological space with underlying set $C = C_1 \cup C_2$, where $C_i$ is the circle of radius $i$ and centre $0$ in the complex plane. The basic open sets are:
$\{ ...
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Is the Alexandroff double circle compact and Hausdorff?
I recently encountered the Alexandroff double circle. The underlying set is $C = C_1 \cup C_2$, where $C_i$ is the circle of radius $i$ and centre $0$ in the complex plane. The basic open sets are:
$\{...
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What do open sets look like in the Alexandroff double cirlce?
I recently encountered the following topological space, called the Alexandroff double cirlce:
The underlying set is $C = C_1 \cup C_2$, where $C_i$ is the circle of radius $i$ and centre $0$ in the ...
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