Rectifiable Spaces
by
Alexandra S. Gul'ko

The notion of a rectifiable space is a generalization of the notion of a topological group. A topological space X is said to be rectifiable or a space with rectifiable diagonal provided that there are a surjective homomorphism \Phi: X² --> X² and an element e in X such that \pi₁ o \Phi = \pi₁ and for any x in X the equality \Phi(x, x) = (x, e) is fulfilled, where \pi₁: X² --> X is the projection to the first coordinate.

Theorem 1 Let X be a rectifiable first countable T₀ space. Then X is metrizable.

Theorem 2 Let X be a rectifiable space. Then

1. \pi\chi(X) = \chi(X);
2. w(X) = d(X) ·\chi(X);
3. w(X) <= k(X) ·\chi(X);
4. If X is locally compact, then w(X) = k(X) ·\chi(X);
5. \piw(X) = w(X);
6. \psi(X) = \Delta(X).

Some corollaries and examples are also presented.

Date received: June 24, 1996

Copyright © 1996 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caah-29.