Continuity and adherence in topology
12490
A map is continuous if and only if for every set, the image of closure is contained in the closure of image
88028
Topology - closures of intervals with the order topology
60383
What is the intuition for the point-set topology definition of continuity?
133422
How to prove the continuity of an induced map; $g_* : C(X, Y) \rightarrow C(X, R)$, induced from the map $g \in C(Y, R)$, endowed with fine topology.
140929
Increasing, continuous function implies connectivity and viceversa.
64619
Continuity of a function of product spaces
151051
connectedness of uniform topology
153256
Compact topological space with closed graph implies continuity
57468
Continuous homorphisms between topological groups.
59519
What about the continuity of these functions in the uniform topology?
143951
Can we determine uniform continuity from graphs?
6415
Distance function is continuous in topology induced by the metric
154572
Continuity of a function at an isolated point
84104
Definition of neighborhood and open set in topology
113498
Example of topological spaces where sequential continuity does not imply continuity
158221
Prob. 4 (a), Sec. 20 in Munkres' Topology, 2nd ed: Are these functions continuous in the product, uniform, and box topologies?
114856
Universal property of initial topology