Topology exercise: how to prove this equivalent definition of continuity
12490
A map is continuous if and only if for every set, the image of closure is contained in the closure of image
36227
Show continuity or uniform continuity of $\phi: (C([0,1];\Bbb R ),||\cdot||_\infty )\to (\Bbb R, |\cdot | )$
147788
Why is every map to an indiscrete space continuous?
102315
difference of uniform continuity and continuity of map
39010
Metrization of the cofinite topology
95327
Lipschitz and uniform continuity
135025
Axiomatization of a Topology using the Boundary
88028
Topology - closures of intervals with the order topology
153730
Show that $f(x)=x^2$ is continuous at $a=2$ using the $\delta-\epsilon$ definition of continuity.
153424
Proof of "continuity from above" and "continuity from below" from the axioms of probability
85242
Deciding whether two metrics are topologically equivalent in the space $C^1([0,1])$
32205
Topology on the real numbers such that all polynomials are continuous but cosine is not continuous
6415
Distance function is continuous in topology induced by the metric
59289
Nested Sequence of Topological Space and the Coherent Topology; Munkres Topology 35.9
118207
Prove that the product of two continuous functions is continuous
153952
A map between metric spaces preserving convergent sequences is continuous
106298
Prove that some topology is not metrizable