Showing a set involving complement is a topological space.
7678
Show "countable complement topology" is a topology
31266
Proof of "the continuous image of a connected set is connected"
120273
Showing that a collection of sets is a $\sigma$-algebra: either set or complement is countable
13848
Showing that if a subset of a complete metric space is closed, it is also complete
15480
Open set in a metric space is union of closed sets
59424
Showing that $B=\{(x,y) \in \Bbb{R^2} \mid \ xy>0 \}$ is an open set
62911
Let $(X,\tau)$ be a connected topological space, $Y\subset X$ connected and $U\subset X\setminus Y$ clopen. Prove that $ Y \cup U$ is connected
73154
Compact subset in colimit of spaces
77791
Proving an inclusion related to algebraic sets and interpreting it
118765
A topological space is locally compact then here is an open base at each point has all of its set with compact closure
6523
Prove that the space has a countable dense subset
125962
The set $A'$ is closed in a $T_1$ space
66239
Verifying that a certain collection of intervals of $\mathbb R$ forms a topology
55484
Proving that the map from a topological space to a fiber bundle is open.
24050
Characterization of the Closure of a Set
85870
Show this set is a base for some topology on $\mathbb{Z}$
149317
An open subset of $\mathbb{R}$ is an at-most-countable union of disjoint open intervals