Can two different topologies have the same basis?
69204
When I prove two topologies are same, is it sufficient to prove they have same basis? If so,Why?
21938
describing all possible topologies on a set
66239
Verifying that a certain collection of intervals of $\mathbb R$ forms a topology
128481
Can two different topological spaces cover each other?
39010
Metrization of the cofinite topology
135783
Let $T$ and $T^{'}$ be topologies on set $X$ such that $T \leq T^{'}$. If $(X,T^{'})$ is path-connected, is $(X,T)$ path connected?
81423
Completeness and Topological Equivalence
109374
Is the Discrete Topology on $X$ the Only One Containing All Infinite Subsets of $X$?
50584
Parallel universes: are there an infinite amount of universes?
43964
When can a pair of groups be embedded in each other?
151950
Why is indiscrete topology unmetrizable?
135025
Axiomatization of a Topology using the Boundary
154259
Countinuity of the identity map between different topologies
85870
Show this set is a base for some topology on $\mathbb{Z}$
108226
Are these bases for a topology?
114523
The coarsest such topology on $\mathbb{R^{2}}$ is the usual topology
41047
Subspace Topology of a subset