query: Singletons closed in infinite T1 Product Topology?
positive_passages.docid: 16512
positive_passages.text: Product of $T_1$ spaces is $T_1$
negative_passages.docid: 99341
negative_passages.text: Basic question: closure of irreducible sets
negative_passages.docid: 77563
negative_passages.text: Homeomorphism between spaces equipped with cofinite topologies
negative_passages.docid: 153573
negative_passages.text: Counter Example for the union of any number of compact sets is compact in T2-spaces
negative_passages.docid: 48557
negative_passages.text: Product of connected spaces
negative_passages.docid: 34966
negative_passages.text: Is the product of closed subgroups in topological group closed?
negative_passages.docid: 41339
negative_passages.text: Why do we require a topological space to be closed under finite intersection?
negative_passages.docid: 26563
negative_passages.text: Help completing a proof regarding an infinite family of nested closed subsets in a compact metric space
negative_passages.docid: 65196
negative_passages.text: Gluing Lemma for Closed Sets: Infinite Cover Counter-Example
negative_passages.docid: 85782
negative_passages.text: UFDs are integrally closed
negative_passages.docid: 144383
negative_passages.text: The closure of a connected set in a topological space is connected
negative_passages.docid: 56171
negative_passages.text: Is $K(X)$ never algebraically closed?
negative_passages.docid: 27661
negative_passages.text: The closed graph theorem in topology
negative_passages.docid: 123828
negative_passages.text: finite and infinite product of discrete space
negative_passages.docid: 60678
negative_passages.text: Does 'A countable infinite Cartesian product of countable sets is not necessarily countable' violate induction principle?
negative_passages.docid: 90816
negative_passages.text: Why does the product topology allow proper subsets for only finitely many elements?
negative_passages.docid: 99353
negative_passages.text: Topology on cartesian product and product topology.