query: Simple question on connectedness in a subspace
positive_passages.docid: 28641
positive_passages.text: Suppose $Y\subset X$ and $X,Y$ are connected and $A,B$ form separation for $X-Y$ then, prove that $Y\cup A$ and $Y\cup B$ are connected
negative_passages.docid: 23225
negative_passages.text: Union of connected subsets is connected if intersection is nonempty
negative_passages.docid: 42811
negative_passages.text: Product of path connected spaces is path connected
negative_passages.docid: 39746
negative_passages.text: How to prove that given set is a connected subset of the space of matrices?
negative_passages.docid: 41347
negative_passages.text: The dimension of the intersection of two vector subspaces
negative_passages.docid: 22295
negative_passages.text: Subspace of a separable space is separable
negative_passages.docid: 58285
negative_passages.text: Is it true that if $X$ is connected, then for every nonempty proper subset $A$ of $X$, we have $\mathbf{Bd} \ne \emptyset$
negative_passages.docid: 38516
negative_passages.text: Show a subset is subspace of a vectorspace and find the dimension
negative_passages.docid: 108052
negative_passages.text: Does any connected metrizable space with more than one element have uncountably many open sets, each generating a connected subspace?
negative_passages.docid: 35625
negative_passages.text: Direct sum of orthogonal subspaces
negative_passages.docid: 151719
negative_passages.text: Connected set in $\mathbb{S}^1$
negative_passages.docid: 45337
negative_passages.text: Suppose that $V, W$ are closed in $X$ and that $V\cap W, V\cup W$ are connected. Show that $V$ and $W$ are connected.
negative_passages.docid: 93623
negative_passages.text: Showing that every connected open set in a locally path connected space is path connected
negative_passages.docid: 151051
negative_passages.text: connectedness of uniform topology
negative_passages.docid: 146364
negative_passages.text: $X$ is connected iff $\forall A\subset X,$ $\partial A\neq\emptyset$
negative_passages.docid: 147197
negative_passages.text: Number of connected components of the complement of a compact
negative_passages.docid: 95513
negative_passages.text: Proving $W$ is a subspace of $P_{2}$