Atlas: Hereditary Lindelof Number is Preserved by $l$-Equivalence by V. V. Tkachuk

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The Eleventh Summer Conference on General Topology and Applications
August 10-13, 1995
University of Southern Maine
Gorham, ME, USA

Organizers
J. Baumgartner, D. Briggs, J. deBakker, B. Flagg, G. Gruenhage, M. Guay, Y. Kong, R. Kopperman, S. Shore, J. Rutten, J. Vaughan

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Hereditary Lindelöf Number is Preserved by l-Equivalence
by
V. V. Tkachuk
UAM-Iztapalapa

Tychonoff spaces X and Y are l-equivalent if C_p(X) is linerly homeomorphic to C_p(Y). The property which is preserved by l-equivalence is called l-invariant. It is known that the cardinality, density, the network weight and covering dimension are l-invariant, while the weight, metrizability and many others aren't. It is ususally simple to prove that a multiplicative topological property is l-invariant. If it is not multiplicative, then in most cases it is not invariant, or if it is then the proof would be pretty difficult.

Practically every l-invariant non-multiplicative property requires an individual method of proof. The latest breakthrough in this direction was N.V. Velichko's result on l-invariance of the Lindelöf number which was established in 1991.

The author succeeded to prove that the hereditary Lindelöf number is l-invariant in ZFC. Under some set-theoretic assumptions the l-invariance of the hereditary separability was established. Other results on l-invariant properties will be presented and discussed.

Date received: April 12, 1996