Two curves (boundaries of $2$-dimensional disks) of constant width in the plane, whose interiors intersect, must meet in an even or infinite number of omponents. Some new constant width curves are constructed. C0rollariesand partial converses suggest severalopen questions.

In this paper a cobordism theory for line bundles over oriented manifolds, with $w_{2}(\mathrm{Base})=w_{1}^{2}(\mathrm{bundle})$, is studied. The cobordism groups $\Lambda_{n}$ are computed. A homomorphism $$\Lambda_{n} \rightarrow \Omega_{n}^{S_{pin}}(Z_{2})$$ is given, and it is shown that this is a monomorphism mod torsion.

Let $S$ be an arbitrary infinite set and let $G$ be the group of finitely supported permutations of $S$; give $G$ the topology of pointwise convergence on $S$. Let $B$ be a reflexive Banach space and let $\Gamma$ be a continuous representation of $G$ on $B$ such that $||\Gamma(g)||\leq M$ for all $g \epsilon G$ for some fixed positive number $M$. Through the use of a canonically defined dense subspace of cofinite vectors, it is shown that $\Gamma$ is strongly continuous and contains an irreducible subrepresentation. An equivalence relation of cofinite equivalence of representations is defined; if $\Gamma$ is irreducible, then $\Gamma$ is cofinitely equivalent to an irreducible weakly continuous unitary representation of $G$ on a Hilbert space.