Given a topological space $X$, why are both $X$ and $\emptyset$ open and closed?
39020
Why is empty set an open set?
49721
Prove the empty set is closed for a metric space (X,d).
110744
How to prove that a compact set in a Hausdorff topological space is closed?
143457
Is product of two closed sets closed?
93750
Can a set be neither open nor closed?
59654
Show that in a discrete metric space, every subset is both open and closed.
58285
Is it true that if $X$ is connected, then for every nonempty proper subset $A$ of $X$, we have $\mathbf{Bd} \ne \emptyset$
2198
Maps from subsets of $\mathbb{R}^2$ that are either open/closed/continuous
88205
How can I define a topology on the empty set?
28523
When would the intersection of the empty set mean anything?
123498
Is "empty set" an element of a set?
118851
$X$ be a Hausdorff topological space , let $f:X \to X$ be a continuous map such that $f\circ f=f$ , then is $f(X)$ is closed in $X$ ?
138202
Every open set in $\mathbb{R}$ is a countable union of closed sets
2056
A space is $T_{0}$ if and only if the closures of singletons are distinct
44623
Closed set as a countable intersection of open sets
74860
Why is the empty set a subset of every set?
123897
Sum of two open sets is open?