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Questions tagged [moore-plane]

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6
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3answers
223 views

Separating closed sets in Moore plane / Niemytzki plane (Topology)

I spent the last few days trying to solve this exercise with little success, so I really hope someone here might be able to assist: Denote Moore plane by $M$, the $x$-axis by $R$ and the upper ...
0
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2answers
25 views

How do I prove that there exists a bijection from power set of $D$ to $C'\subseteq C.$

I was proving the Moore's Plane $(X,\mathscr T)$ is not normal. Using the theorem. Let $C=\{(x,y)\in X:y=0\}$ be a closed and relatively discrete subset of $X$. Let $D=\{(x,y)\in X:x\in \mathbb Q \...
5
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1answer
809 views

Moore plane / Niemytzki plane (Topology)

I am supposed to show that by adding a point to the Moore plane, that the subspace of a $T_4$-space is not necessarily a $T_4$-space. I do know that the Moore plane is NOT a $T_4-$space. Does anybody ...
0
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1answer
307 views

Moore plane $\tau$ closure

May you could help me finding the simple $\tau$-closures of the subsets $A=\mathbb Q\times \{1\}$ and $B=Q\times \{0\}$ Backround: We consider a Moore plane $\Gamma:=\{(x,y)\in\mathbb R^2: y\ge 0\}$ ...