Proof that a continuous function maps connected sets into connected sets
31266
Proof of "the continuous image of a connected set is connected"
19566
Continuous images of compact sets are compact
125682
Proof verification: the product of two continuous functions is continuous
158221
Prob. 4 (a), Sec. 20 in Munkres' Topology, 2nd ed: Are these functions continuous in the product, uniform, and box topologies?
99179
Continuous function with compact domain has continuous inverse
156520
Intervals are connected and the only connected sets in $\mathbb{R}$
45276
Continuous map on $S^2$
55486
Topological proof to show a complement set of a set is polygonally connected
136583
Infimum is a continuous function, compact set
40297
Proof of uniform limit of Continuous Functions
12490
A map is continuous if and only if for every set, the image of closure is contained in the closure of image
108394
Proof of that every interval is connected
128069
Continuity in Slices + Mapping Compact Sets to Compact Sets = Continuous
143174
property of continuous function
36149
A uniformly continuous function maps bounded set to bounded sets
70645
Borel set preserved by continuous map
117502
Proving that a certain continuous function is surjective.