Basic Topological problem on closed sets
12490
A map is continuous if and only if for every set, the image of closure is contained in the closure of image
158155
Is set of isolated points of S closed?
111360
Topological spaces in which every proper closed subset is compact
144383
The closure of a connected set in a topological space is connected
78117
Closed property of nonempty finite set
151719
Connected set in $\mathbb{S}^1$
158569
Proving a particular subset of $R^n$ is closed
106298
Prove that some topology is not metrizable
84512
The preimage of continuous function on a closed set is closed.
148213
Given a topological space $X$, why are both $X$ and $\emptyset$ open and closed?
153495
Continuous function does not map closed set to closed set
130975
Given a pair of continuous functions from a topological space to an ordered set, how to prove that this set is closed?
15480
Open set in a metric space is union of closed sets
106957
Compact sets are closed?
70048
In which topologies do open sets maintain open under countable or arbitrary intersection?
127900
Interior of closure of open set in topological space
110957
No non-trivial clopen sets in $\mathbb{R}$? How to give a direct proof?