Topological spaces compact with respect to a set of filters

• Autorzy: Paolo Lipparini
• Języki publikacji: EN

Abstrakty

EN

If is a family of filters over some set I, a topological space X is sequencewise -compact if for every I-indexed sequence of elements of X there is such that the sequence has an F-limit point. Countable compactness, sequential compactness, initial κ-compactness, [λ; µ]-compactness, the Menger and Rothberger properties can all be expressed in terms of sequencewise -compactness for appropriate choices of . We show that sequencewise -compactness is preserved under taking products if and only if there is a filter such that sequencewise -compactness is equivalent to F-compactness. If this is the case, and there exists a sequencewise -compact T 1 topological space with more than one point, then F is necessarily an ultrafilter. The particular case of sequential compactness is analyzed in detail.

Słowa kluczowe

EN

Filter; Ultrafilter convergence; Sequencewise -compactness; Preservation under products; Comfort pre-order; Sequential compactness

Kategorie tematyczne

• 03E05: Other combinatorial set theory
• 54B10: Product spaces
• 54A20: Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)
• 54D20: Noncompact covering properties (paracompact, Lindel\"of, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 7
• Strony: 991-999

Daty

wydano

2014-07-01

online

2014-04-03

Twórcy

autor

Paolo Lipparini

• II Università di Roma (Tor Vergata)

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-013-0398-2