Example of an interesting topological space that doesn't have a metric
64375
Non-Metrizable Topological Spaces
88099
Not $\sigma$-compact set without axiom of choice
14496
Is there any example of a non-measurable set whose proof of existence doesn't appeal to the Axiom of choice?
122121
Is there a vector space that cannot be an inner product space?
150961
An example for a homomorphism that is not an automorphism
80524
Path-connected and locally connected space that is not locally path-connected
52014
Showing $(C[0,1], d_1)$ is not a complete metric space
90628
The metric spaces are Tychonoff spaces
108408
Example of quotient mapping that is not open
32819
Looking for examples of first countable, compact spaces which is not separable
154009
Closed, simply connected manifolds which are not spheres
147961
Characterizing simply connected spaces
115350
An example of a Banach space isomorphic but not isometric to a dual Banach space
132571
Local homeomorphisms which are not covering map?
151984
Proving the existence of a metric space
100436
Examples of nowhere continuous functions
129623
A shrinking map that is not a contraction no fixed point.