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Relatively maximal convergences

Szymon Dolecki, Michel Pillot (1998)

Bollettino dell'Unione Matematica Italiana

Topologie, pretopologie, paratopologie e pseudotopologie sono importanti classi di convergenze, chiuse per estremi superiori (superiormente chiuse) ed inoltre caratterizzabili mediante le aderenze di certi filtri. Convergenze J -massimali in una classe superiormente chiusa D J , cioè massimali fra le D -convergenze aventi la stessa imagine per la proiezione su J , svolgono un ruolo importante nella teoria dei quozienti; infatti, una mappa J -quoziente sulla convergenza J -massimale in D è automaticamente...

S -cubes

Jozef Tvarožek (1986)

Mathematica Slovaca

Sequential compactness vs. countable compactness

Angelo Bella, Peter Nyikos (2010)

Colloquium Mathematicae

The general question of when a countably compact topological space is sequentially compact, or has a nontrivial convergent sequence, is studied from the viewpoint of basic cardinal invariants and small uncountable cardinals. It is shown that the small uncountable cardinal 𝔥 is both the least cardinality and the least net weight of a countably compact space that is not sequentially compact, and that it is also the least hereditary Lindelöf degree in most published models. Similar results, some definitive,...

Tanaka spaces and products of sequential spaces

Yoshio Tanaka (2007)

Commentationes Mathematicae Universitatis Carolinae

We consider properties of Tanaka spaces (introduced in Mynard F., More on strongly sequential spaces, Comment. Math. Univ. Carolin. 43 (2002), 525–530), strongly sequential spaces, and weakly sequential spaces. Applications include product theorems for these types of spaces.

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