Displaying similar documents to “The sequentiality is equivalent to the ℱ -Fréchet-Urysohn property”

Topological spaces compact with respect to a set of filters

Paolo Lipparini (2014)

Open Mathematics

Similarity:

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...

Closure spaces and characterizations of filters in terms of their Stone images

Anh Tran Mynard, Frédéric Mynard (2007)

Czechoslovak Mathematical Journal

Similarity:

Fréchet, strongly Fréchet, productively Fréchet, weakly bisequential and bisequential filters (i.e., neighborhood filters in spaces of the same name) are characterized in a unified manner in terms of their images in the Stone space of ultrafilters. These characterizations involve closure structures on the set of ultrafilters. The case of productively Fréchet filters answers a question of S. Dolecki and turns out to be the only one involving a non topological closure structure. ...