Induced topologies by Metric Spaces continuous
6415
Distance function is continuous in topology induced by the metric
70645
Borel set preserved by continuous map
150987
Showing that the product and metric topology on $\mathbb{R}^n$ are equivalent
124179
Proof that every metric space is normal
144400
Are compact subsets of metric spaces closed and bounded?
15480
Open set in a metric space is union of closed sets
147788
Why is every map to an indiscrete space continuous?
88028
Topology - closures of intervals with the order topology
99816
Existence of Topologically Transitive Maps on nice Metric Spaces
60383
What is the intuition for the point-set topology definition of continuity?
27517
Isometry in compact metric spaces
15487
Continuous function from a connected set?
49374
Closure of a subset in a metric space
125580
Proving that every countable metric space is disconnected?
36149
A uniformly continuous function maps bounded set to bounded sets
117897
A homomorphism induces a continuous map from ${\rm Spec}(A') \to {\rm Spec}(A)$.
64487
Continuous function and dense set