Paracompactness of locally compact Hausdorff spaces.

Finney, Ross Lee; Rotman, Joseph

doi:10.1307/mmj/1029000524

Cited by 8 publications

(4 citation statements)

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“…To prove the next theorem we will use a well-known result, Lemma 3.3.2 (See [24]). If E → M is a finite rank vector bundle over a manifold, then Γ c (E) is a projective C ∞ (M)-module.…”

Section: Renormalizations Feynman Measuresmentioning

confidence: 99%

On the renormalization group of quantum field theory (after R. Bocherds)

Palau

2017

Preprint

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Section: Renormalizations Feynman Measuresmentioning

confidence: 99%

On the renormalization group of quantum field theory (after R. Bocherds)

Palau

2017

Preprint

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“…Then B is a commutative regular ring and I is a non-projective ideal of B (cf. Bkouche [3], Finney and Rotman [5]). In the particular case where X is the example above, I is the union of the increasing chain of principal ideals corresponding to the intervals [0, α], for α < ω 1 .…”

Section: Proposition 43 Let a And B Be Chains And Letmentioning

confidence: 99%

A non-coordinatizable sectionally complemented modular lattice with a large Jónsson four-frame

Wehrung

2011

Advances in Applied Mathematics

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A sectionally complemented modular lattice L is coordinatizable if it is isomorphic to the lattice L(R) of all principal right ideals of a von Neumann regular (not necessarily unital) ring R. We say that L has a large 4-frame if it has a homogeneous sequence (a 0 , a 1 , a 2 , a 3 ) such that the neutral ideal generated by a 0 is L. Jónsson proved in 1962 that if L has a countable cofinal sequence and a large 4-frame, then it is coordinatizable; whether the cofinal sequence assumption could be dispensed with was left open. We solve this problem by finding a non-coordinatizable sectionally complemented modular lattice L with a large 4-frame; it has cardinality ℵ 1 . Furthermore, L is an ideal in a complemented modular lattice L ′ with a spanning 5-frame (in particular, L ′ is coordinatizable).Our proof uses Banaschewski functions. A Banaschewski function on a bounded lattice L is an antitone self-map of L that picks a complement for each element of L. In an earlier paper, we proved that every countable complemented modular lattice has a Banaschewski function. We prove that there exists a unit-regular ring R of cardinality ℵ 1 and index of nilpotence 3 such that L(R) has no Banaschewski function.

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“…In the case where F = R, Theorem 10.3 is known [50], [64]. The following result was proved by Brooksher [53] in the case F = IR.…”

Section: S(coo) C_ Xmentioning

confidence: 99%