By T. L. Cleave
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Additional resources for A Theory That Any Organism Is a Single Chemical Molecule. Put Forward as the Key to the Problem of the Causation of Neoplasms
I is an Fσ P-ideal if and only if there is a lscsm ϕ such that I = Exh(ϕ) = F in(ϕ). In particular, all analytic P-ideals are Fσδ . 5. MAD families and ultraﬁlters. Given two inﬁnite subsets A, B of ω we say A and B are almost disjoint if A ∩ B is ﬁnite. A family A of inﬁnite subsets of ω is an almost disjoint family if A and B are almost disjoint for any A, B distinct elements of A. e. an almost disjoint family such that for every inﬁnite set X ⊆ ω there is an A ∈ A such that A ∩ X is inﬁnite.
Note that the class D of all D-spaces satisﬁes the hypotheses of the theorem, so any submetacompact D-scattered space is D. Any scattered space and any locally D-space is D-scattered. 5. 6. (1) Are (sub)metalindel¨ of scattered spaces D? 2 have a positive answer in the class of scattered spaces? 4 for discussion of a direct proof (without using games) of this result. 18 6 GARY GRUENHAGE Another nice illustration of game theory in this area involves the Menger property, which says that, given a countable sequence Un , n ∈ ω, of open covers of X, one can select for each n a ﬁnite subcollection Vn of Un such that n∈ω Vn is a cover.
24 12 GARY GRUENHAGE 7. Mappings There are only a small number of results on mappings of D-spaces. 1.  If X is a D-space, then so is every closed image of X and every perfect pre-image of X. Note that fact that the product of a D-space with a compact space is D is a corollary to the result on perfect pre-images. As was pointed out in , quotient or even open images of D-spaces need not be D. Any ﬁrst countable space is the open image of a metrizable space, but of course there are ﬁrst-countable spaces which are not D-spaces.
A Theory That Any Organism Is a Single Chemical Molecule. Put Forward as the Key to the Problem of the Causation of Neoplasms by T. L. Cleave