query: If $L$ is a straight line then what is the topology that $L$ inherits as a subspace from $\mathbb{R}_l \times \mathbb{R}$
positive_passages.docid: 146445
positive_passages.text: What Topology does a Straight Line in the Plane Inherit as a Subspace of $\mathbb{R_l} \times \mathbb{R}$ and of $\mathbb{R_l} \times \mathbb{R_l}$
negative_passages.docid: 106298
negative_passages.text: Prove that some topology is not metrizable
negative_passages.docid: 134065
negative_passages.text: A question about an $n$-dimensional subspace of $\mathbb{F}^{S}$.
negative_passages.docid: 60684
negative_passages.text: Determine whether the set $W$ is a subspace in $\mathbb{R}^{3}$
negative_passages.docid: 31617
negative_passages.text: Is the collection $\tau_\infty = \{U:X-U$ is infinite or empty or all of $X\}$ a topology on $X$?
negative_passages.docid: 126192
negative_passages.text: Connected, locally connected, path-connected but not locally path-connected subspace of the plane
negative_passages.docid: 100437
negative_passages.text: Classification of connected subsets of the real line (up to homeomorphism)
negative_passages.docid: 66548
negative_passages.text: proving topological equivalence
negative_passages.docid: 137438
negative_passages.text: Restrict a metric, gives same topology as subspace topology from larger space $X$
negative_passages.docid: 13993
negative_passages.text: Can we prove $ℝ^n ∖ \{\text{straight line}\}$ and $ℝ^n ∖ \text{\{an axis\}}$ homeomorphic by proving their complements homeomorphic?
negative_passages.docid: 30796
negative_passages.text: Is the set of irrationals separable as a subspace of the real line?
negative_passages.docid: 101712
negative_passages.text: Let $X$ be obtained by removing finitely many lines from $\mathbb{R}^3$. How do I prove $X$ is connected?
negative_passages.docid: 41690
negative_passages.text: Products of Continuous functions: Topology
negative_passages.docid: 135025
negative_passages.text: Axiomatization of a Topology using the Boundary
negative_passages.docid: 111838
negative_passages.text: Prove that a standard torus is diffeomorphic to $ \mathbb S^1\times \mathbb S^1$
negative_passages.docid: 151051
negative_passages.text: connectedness of uniform topology
negative_passages.docid: 139334
negative_passages.text: Determining the existence or non-existence of Non Trivial Ideals of $L(V)$