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For questions relating to path-connected topological spaces, that is, spaces where any two points can be connected by a path.

1 vote
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Two questions on path connected spaces

Is it true to say that a compact hausdorff space $X$ is path connected if and only if for every continuous function $f:X\to \mathbb{C}$, we have $f(X)\subset \mathbb{C}$ is path connected? …
Ali Taghavi's user avatar
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Can we classify the general linear maps such that for a fixed matrix $A \in M_n(\mathbb R)$ ...

One can not say that $\mathcal E$ is always connected. For $n=3, $(and similarly $n>3$) let $A$ be a matrix with $a_{i1}=1,\quad \forall i \in \{1,2,\ldots,n\} $ Then $\mathcal E$ conta …
Ali Taghavi's user avatar