Axiom of Choice Page 1 Horst Herrlich ฀123 Lecture N otes in M athem atics 1876 Axiom of
Choice Page 2 Lecture Notes in Mathematics 1876 Editors: J.-M. Morel, Cachan F. Takens …

In the absence of the axiom of choice, the set-theoretic status of many natural statements
about metrizable compact spaces is investigated. Some of the statements are provable in ZF …

A generalized topology in a set X is a collection Cov X of families of subsets of X such that
the triple (X,⋃ Cov X, Cov X) is a generalized topological space (a gts) in the sense of Delfs …

It is shown that for compact metric spaces (X, d) the following statements are pairwise
equivalent:“X is Loeb”,“X is separable”,“X has a we ordered dense subset”,“X is second …

It is a well established fact that in Zermelo-Fraenkel set theory, Tychonoff's Theorem, the
statement that the product of compact topological spaces is compact, is equivalent to the …

T:ISSUESSPRINGERk_AML _8 Page 1 Digital Object Identifier (DOI): 10.1007/s001530100094
Arch. Math. Logic 40, 569–580 (2001) Mathematical Logic Kyriakos Keremedis Disasters in …

We show that:(i) If every sequentially compact metric space is countably com $ pact then for
every infinite set X,[X]! is Dedekind $ infinite. In particular, every infinite subset of R is …

A P-space is a topological space whose every G_δ-set is open. In this article, basic
properties of P-spaces are investigated in the absence of the Axiom of Choice. New weaker …

NON-CONSTRUCTIVE PROPERTIES OF THE REAL NUMBERS Paul Howard, Kyriakos
Keremedis, Jean E. Rubin, Adrienne Stanley, and Eleftherio Page 1 NON-CONSTRUCTIVE …

A topological space is iso-dense if it has a dense set of isolated points, and it is scattered if
each of its non-empty subspaces has an isolated point. In ZF (ie Zermelo–Fraenkel set …