Any collection of subsets of a set is a subbasis for a topology
101497
Any class of a nonempty $X$ generates a base for a topology on $X$.
85099
How many subsets of $\mathbb{N}$ have the same cardinality as $\mathbb{N}$?
19856
Prove that a subset of a separable set is itself separable
109682
Proposed proof of: If $A \subset B \subset \bar{A}$ and $A$ is connected, then $B$ is connected
66334
How is every subset of the set of reals with the finite complement topology compact?
130156
Image of the union and intersection of sets.
74311
Proving that the Intersection of any Collection of Compact Sets is Compact
142583
Subsets of the Cantor set
90816
Why does the product topology allow proper subsets for only finitely many elements?
111008
Show that $X $ is a infinite set ,it is connected in the finite complement topology?
97697
Countable union of sets of cardinality $c$ has cardinality $c$
12436
The cardinality of the set of all finite subsets of an infinite set
40071
What is the cardinality of the set of all topologies on $\mathbb{R}$?
63276
Is an arbitrary union of a chain of countable sets countable?
146664
The union of two linearly independent subsets
9021
An infinite subset of a countable set is countable
23225
Union of connected subsets is connected if intersection is nonempty