The fiber of a covering space over a connected space has constant cardinality
7665
If $h : Y \to X$ is a covering map and $Y$ is connected, then the cardinality of the fiber $h^{-1}(x)$ is independent of $x \in X$.
79213
Proof about a Topological space being arc connect
120673
Irreducible fibers of a closed subset implies irreducibility
115695
If $X$ is a connected subset of a connected space $M$ then the complement of a component of $M \setminus X$ is connected
136158
$X$ has Indiscrete topology $\implies$ any subset of $X$ is connected
77621
Continuity of function mapping connected set to connected set
121626
Every open cover of the real numbers has a countable subcover (Lindelöf's lemma)
62911
Let $(X,\tau)$ be a connected topological space, $Y\subset X$ connected and $U\subset X\setminus Y$ clopen. Prove that $ Y \cup U$ is connected
7069
On the product of $\mathfrak c$-many separable spaces
16649
Topological space with countable open cover $\{U_\alpha\} $ with each $U_\alpha$ second-countable, is second countable
131890
Totally disconnected space that is not $T_2$
115347
Showing that the fiber of a morphism of schemes over a point is homeomorphic to the preimage
28406
composition of certain covering maps
106534
"Closed subsets of compact space are compact" with an alternative definition of covering
45805
(A question regarding:) the graph associated with an open cover of a topological space.
83163
If $X$ is a connected metric space, then a locally constant function $f: X \to $ M, $M $ a metric space, is constant
93623
Showing that every connected open set in a locally path connected space is path connected