A note on an example by van Mill

Hart, Klaas Pieter; Ridderbos, G.J.F.

doi:10.1016/j.topol.2004.12.006

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Observed Upper Bounds On Noetherian Cardinal Functions2

Claim Because R Is a Retraction And ω Is A Discrete Open Su1

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Cited by 9 publications

(3 citation statements)

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“…Suppose X, Y p p∈X , f p p∈X , and Z are as in Definition 2. 8. Then χN t( p, y , Z) ≤ N t(X)χN t(y, Y p ) for all p, y ∈ Z.…”

Section: Observed Upper Bounds On Noetherian Cardinal Functionsmentioning

confidence: 98%

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Noetherian types of homogeneous compacta and dyadic compacta

Milovich

2008

Topology and its Applications

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The Noetherian type of a space is the least $\kappa$ such that it has a base that is $\kappa$-like with respect to containment. Just as all known homogeneous compacta have cellularity at most $2^\omega$, they satisfy similar upper bounds in terms of Noetherian type and related cardinal functions. We prove these and many other results about these cardinal functions. For example, every homogeneous dyadic compactum has Noetherian type $\omega$. Assuming GCH, every point in a homogeneous compactum $X$ has a local base that is $c(X)$-like with respect to containment. If every point in a compactum has a well-quasiordered local base, then some point has a countable local $\pi$-base.Comment: 30 page

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“…Suppose X, Y p p∈X , f p p∈X , and Z are as in Definition 2. 8. Then χN t( p, y , Z) ≤ N t(X)χN t(y, Y p ) for all p, y ∈ Z.…”

Section: Observed Upper Bounds On Noetherian Cardinal Functionsmentioning

confidence: 98%

“…Van Mill's construction has been generalized by Hart and Ridderbos [8]. They show that one can produce an exceptional homogeneous compactum with weight c and π-weight ω by carefully resolving each point of 2 ω into a fixed space Y satisfying the following conditions.…”

Section: Observed Upper Bounds On Noetherian Cardinal Functionsmentioning

confidence: 99%

Noetherian types of homogeneous compacta and dyadic compacta

Milovich

2008

Topology and its Applications

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show abstract

“…Van Mill's Theorem 4.2 is directly cited in [2] and indirectly used in [4] and [5]. However, none of these papers use Van Mill's proof of Theorem 4.2.…”

Section: Claim Because R Is a Retraction And ω Is A Discrete Open Sumentioning

confidence: 99%