Let $G$ be a topological group and $\mathcal{B}$ its Baire $\sigma$-algebra (i.e. the smallest $\sigma$-algebra for which all continuous functions $G\rightarrow\mathbb{R}$ are measurable). Consider the product map $\cdot :G\times G\rightarrow G$ given by $(g,h)\mapsto g \cdot h$. Question: Is the...

Let $X$ be a singular, projective (complex) variety of dimension $n$ with at worst isolated singularities. We know that taking cup-product with the cohomology class of $X$ induces a morphism from the cohomology group to the Borel-Moore homology: $$ \cap [X]: H^{2p}(X) \to H_{2n-2p}^{\mathrm{BM}}(...