Characterization of open sets
73368
Does this proof that every open set in a metric space is a union of open balls use the axiom of choice?
127900
Interior of closure of open set in topological space
15645
Is convex open set in $\mathbb{R}^n$ is regular?
46788
Compact open topology on space of continuous maps from a discrete space is a product
15480
Open set in a metric space is union of closed sets
52388
The equivalence of open-set definition of continuous mappings to the $\epsilon-\delta$ definition
110957
No non-trivial clopen sets in $\mathbb{R}$? How to give a direct proof?
69283
The limit points of an open interval (open set)
114608
Proof concerning regular space: there exist a closed set contained in any open set containing $x$
64861
Intersection of open affines can be covered by open sets distinguished in *both*affines
129081
Proof that convex open sets in $\mathbb{R}^n$ are homeomorphic?
78117
Closed property of nonempty finite set
100437
Classification of connected subsets of the real line (up to homeomorphism)
84437
Prove that the projection $p_i$ from the product space $X_I S_i \tau$ into $S_i \tau_i$ is open for each $i \in I$
32723
Open sets and holomorphic functions in Complex analysis
50506
What concept does an open set axiomatise?
99236
Interior of closure of an open set