Why, in topology, is continuity defined with inverse images?
90745
Why aren’t continuous functions defined the other way around?
135863
Is the graph of a continuous function homeomorphic to its domain?
15487
Continuous function from a connected set?
52388
The equivalence of open-set definition of continuous mappings to the $\epsilon-\delta$ definition
150796
Subspace topology and order topology (2)
26794
Metrizability of Hausdorff continuous image of compact metric space
122086
continuous function: preimage of closure of a set is closure of preimage
132407
inverse image presheaf property
88205
How can I define a topology on the empty set?
114437
Why is this the basis for the indiscrete topology?
31747
Uniqueness of continuous extension from $A$ to $\overline{A}$ for maps into a Hausdorff space
7036
Is there a bijective continuous function $f: \Bbb R \to \Bbb R$ whose inverse $f^{-1}$ is not continuous?
135025
Axiomatization of a Topology using the Boundary
6415
Distance function is continuous in topology induced by the metric
133265
Definition of continuity at a point
80274
What is the "topology induced by a metric"?
72190
Topological proof on discrete topology where $X$ is infinite