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YCor
YCor
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Let $G$ be a topological group and $H$ its closed subgroup. $K$ and $L$ are open subgroups of $G$ and $H$ respectively. Let $g_{1}, g_{2}\in G$. We assume $L\cap g_{1}K\neq \phi$$L\cap g_{1}K\neq \emptyset$ and $L\cap g_{2}K\neq \phi$$L\cap g_{2}K\neq \emptyset$. Then Isis there an element $x\in H$ (also $x\in L$) such that $L\cap g_{1}K=x(L\cap g_{2}K)$ ?

Let $G$ be a topological group and $H$ its closed subgroup. $K$ and $L$ are open subgroups of $G$ and $H$ respectively. Let $g_{1}, g_{2}\in G$. We assume $L\cap g_{1}K\neq \phi$ and $L\cap g_{2}K\neq \phi$. Then Is there an element $x\in H$ (also $x\in L$) such that $L\cap g_{1}K=x(L\cap g_{2}K)$ ?

Let $G$ be a topological group and $H$ its closed subgroup. $K$ and $L$ are open subgroups of $G$ and $H$ respectively. Let $g_{1}, g_{2}\in G$. We assume $L\cap g_{1}K\neq \emptyset$ and $L\cap g_{2}K\neq \emptyset$. Then is there an element $x\in H$ (also $x\in L$) such that $L\cap g_{1}K=x(L\cap g_{2}K)$ ?

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M masa
M masa
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Left-side cosets of an open subgroup

Let $G$ be a topological group and $H$ its closed subgroup. $K$ and $L$ are open subgroups of $G$ and $H$ respectively. Let $g_{1}, g_{2}\in G$. We assume $L\cap g_{1}K\neq \phi$ and $L\cap g_{2}K\neq \phi$. Then Is there an element $x\in H$ (also $x\in L$) such that $L\cap g_{1}K=x(L\cap g_{2}K)$ ?