New posts in connectedness

If union and intersection of two subsets are connected, are the subsets connected?

general-topology connectedness

Topological space that is not homeomorphic to the disjoint union of its connected components

general-topology examples-counterexamples connectedness

Are the subsets $G^{+}$ and $G^{-}$ connected in $\mathbb{R^{2}}\setminus G$?

general-topology connectedness

The image of a path-connected set under a continuous map is path-connected

general-topology connectedness

Cofinite topology on an infinite set $X$ is connected?

general-topology connectedness

Is the set $\{X \in \mathcal{M}({m \times n}) : \rho(M-NX) < 1\} $ connected?

linear-algebra general-topology connectedness path-connected

Finding simply connected open sets between compact ones and general open ones in $\mathbb R^2$.

real-analysis general-topology connectedness

Tracing a curve along itself - can the result have holes?

general-topology geometry continuity connectedness curves

Family of connected sets, proving union is connected

analysis connectedness

Prove $\mathbb{R}$ is connected

real-analysis general-topology analysis connectedness

Continuity of function mapping connected set to connected set

real-analysis continuity connectedness

Existence of a path between two sides of a square, which is contained in the intersection of two open subsets of it

general-topology geometry connectedness

Is there a short proof for the Intermediate Value Theorem

calculus analysis continuity connectedness

If a closed set does not separate $\mathbb{R}^n$, can one of its connected components separate $\mathbb{R}^n$?

real-analysis general-topology connectedness

Space which is connected but not path-connected

general-topology examples-counterexamples connectedness path-connected

In a metric space X, if A is connected, is its interior connected?

general-topology metric-spaces examples-counterexamples connectedness

Connecting Points in a Region $\Omega \subset \mathbb{C}$ by a Piecewise Smooth Curve

complex-analysis connectedness plane-curves path-connected

Continuous Injective Map $f :\mathbb{S}^2 \rightarrow \mathbb{S}^1$

general-topology continuity connectedness

Are Products of Arc Connected Spaces Arc Connected, or vice versa?

general-topology connectedness

Conditions for a intersection of connected sets to be connected.

general-topology metric-spaces connectedness