## Indestructible properties of S- and L-spaces

**L. Soukup **

Building on a method of U. Abraham and S. Todorcevic
we prove a preservation theorem on certain properties under
c.c.c forcings. Applying this result we show that
(1) an uncountable, first countable, 0-dimensional space
containing only countable and co-countable open subspaces, and (2)
S- and L-groups
can exist under Martin's Axiom.

Key words and phrases: Martin's Axiom, S-space, L-space, S-group, L-group,
first countable, Ostaszewsky-space, preservation, iterated forcing

1991 Mathematics Subject Classification: 03E35, 54E25

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