Must $\emptyset$ be an element of any basis for a topology?
134999
Writing empty set as union of basis elements for a topology.
26008
Why there is a unique empty set?
146364
$X$ is connected iff $\forall A\subset X,$ $\partial A\neq\emptyset$
130361
Basis for a topology with a countable number of sets
128118
Is the cofinite topology on a countable set first countable?
127691
Confusion Regarding Munkres's Definition of Basis for a Topology
65308
Axiom of Choice: Family of non-empty sets mutually disjoint or not?
88823
How can the empty set be open in the definition of the cofinite topology?
27107
intersection of the empty set and vacuous truth
111001
Does weak topology preserve topological vector space structure?
66239
Verifying that a certain collection of intervals of $\mathbb R$ forms a topology
3072
If the empty set is a subset of every set, why isn't $\{\emptyset,\{a\}\}=\{\{a\}\}$?
125502
Empty set literal?
148213
Given a topological space $X$, why are both $X$ and $\emptyset$ open and closed?
110669
Linear span of the empty set
140168
What are the basis for co-countable and co-finite topologies
150825
Is an empty set equal to another empty set?