query: How can a basis of a topological space NOT contain the empty set?
positive_passages.docid: 18828
positive_passages.text: Base and empty set of a topology
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: 3072
negative_passages.text: If the empty set is a subset of every set, why isn't $\{\emptyset,\{a\}\}=\{\{a\}\}$?
negative_passages.docid: 132382
negative_passages.text: Showing a set is nowhere dense in $C([0,1])$
negative_passages.docid: 118824
negative_passages.text: What is the complement of empty set?
negative_passages.docid: 90826
negative_passages.text: Constructing a subset not in $\mathcal{B}(\mathbb{R})$ explicitly
negative_passages.docid: 119649
negative_passages.text: Every metrizable space with a countable dense subset has a countable basis
negative_passages.docid: 4213
negative_passages.text: The set that only contains itself
negative_passages.docid: 28766
negative_passages.text: Intuition behind topological spaces
negative_passages.docid: 65768
negative_passages.text: What is the cardinality of the set of the empty set?
negative_passages.docid: 69204
negative_passages.text: When I prove two topologies are same, is it sufficient to prove they have same basis? If so,Why?
negative_passages.docid: 95897
negative_passages.text: Which sets occur as boundaries of other sets in topological spaces?
negative_passages.docid: 25256
negative_passages.text: When a lattice is a lattice of open sets of some topological space?
negative_passages.docid: 6523
negative_passages.text: Prove that the space has a countable dense subset
negative_passages.docid: 31212
negative_passages.text: The existence of the empty set is an axiom of ZFC or not?
negative_passages.docid: 45508
negative_passages.text: Is the empty set a group?
negative_passages.docid: 41047
negative_passages.text: Subspace Topology of a subset