Ukrainian Mathematical Bulletin

Volume 3, Issue 2, 2006 pp. 259-265.

$\mathcal{H}$-cross-sections of the Semigroup of All Partial Continuous Injections of a Hausdorff Space

Authors: Vasyl' O. Pyekhtyeryev
Author institution: Taras Shevchenko National University, vul. Volodymirs'ka 64, 01033, Kyiv, Ukraine vasiliy@univ.kiev.ua

Summary: In this paper, we prove that if a semigroup, with respect to the composition, of all injective and continuous partial transformations of a Hausdorff space $X$ into itself contains an $\mathcal{H}$-cross-section, then the space $X$ is at most a countable discrete topological space.

Contents Full-Text PDF