real-anylsis: topology, continuous maps, and metric spaces
58004
showing a collection of sets contain all closed sets
49563
Cauchy nets in a metric space
153952
A map between metric spaces preserving convergent sequences is continuous
106256
Continuous mapping on a compact metric space is uniformly continuous
26794
Metrizability of Hausdorff continuous image of compact metric space
2198
Maps from subsets of $\mathbb{R}^2$ that are either open/closed/continuous
140124
The distance function on a metric space
83461
Continuous iff composition with every linear functional is continuous
45276
Continuous map on $S^2$
152976
Real Analysis: open and closed sets
60868
Interplay of Hausdorff metric and Lebesgue measure
85242
Deciding whether two metrics are topologically equivalent in the space $C^1([0,1])$
80274
What is the "topology induced by a metric"?
111119
Distance between any two points in a compact metric space
99121
Extending a continuous map between the boundary of two cells.
66239
Verifying that a certain collection of intervals of $\mathbb R$ forms a topology
128897
Bounded sequence in a metric space