query: topology problem and proof
positive_passages.docid: 131841
positive_passages.text: Difference of closures and closure of difference
negative_passages.docid: 46408
negative_passages.text: Show that the Hausdorff topology is unique in a finite set $X$
negative_passages.docid: 104758
negative_passages.text: First book on algebraic topology
negative_passages.docid: 21938
negative_passages.text: describing all possible topologies on a set
negative_passages.docid: 105996
negative_passages.text: Topology of matrices
negative_passages.docid: 27661
negative_passages.text: The closed graph theorem in topology
negative_passages.docid: 136158
negative_passages.text: $X$ has Indiscrete topology $\implies$ any subset of $X$ is connected
negative_passages.docid: 48557
negative_passages.text: Product of connected spaces
negative_passages.docid: 130361
negative_passages.text: Basis for a topology with a countable number of sets
negative_passages.docid: 76428
negative_passages.text: Exercise $2.1.1$ - Differential Topology by Guillemin and Pollack
negative_passages.docid: 62911
negative_passages.text: Let $(X,\tau)$ be a connected topological space, $Y\subset X$ connected and $U\subset X\setminus Y$ clopen. Prove that $ Y \cup U$ is connected
negative_passages.docid: 116768
negative_passages.text: Problem 5, sec. 13 in Munkres' Topology, 2nd ed.: How to prove the assertion if $\mathscr{A}$ is a subbasis?
negative_passages.docid: 112050
negative_passages.text: Union of ascending chain of Topologies
negative_passages.docid: 99353
negative_passages.text: Topology on cartesian product and product topology.
negative_passages.docid: 156922
negative_passages.text: Proving convergence iff projection converges in product topology
negative_passages.docid: 157742
negative_passages.text: Prove that $U(n)$ is a manifold
negative_passages.docid: 77563
negative_passages.text: Homeomorphism between spaces equipped with cofinite topologies