Every neighborhood is an open set proof question
96522
My own proof of "Every neighborhood is open" (Rudin's definition)
111032
Proof of Sets involving the Cartesian Product
59654
Show that in a discrete metric space, every subset is both open and closed.
70959
Prove that a set $E$ is closed iff it's complement $E^{c}$ is open
59424
Showing that $B=\{(x,y) \in \Bbb{R^2} \mid \ xy>0 \}$ is an open set
81843
Sequences of sets property
33563
Is the axiom of choice used in the proof that every open set is the union of basis elements (Mukres, Lemma 13.1)
108394
Proof of that every interval is connected
28391
Prove the compactness of a set B
62709
Functions that are sets of all function - proofs
123613
Double Complement of a set proof
72190
Topological proof on discrete topology where $X$ is infinite
10472
Is every set a subset?
32441
How to prove or disprove statements about sets
45405
An elementary way to show any bounded subset of $\Bbb{R}^k$ is totally bounded
84104
Definition of neighborhood and open set in topology
77286
Proving set theory question