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C p ( I ) is not subsequential

Viacheslav I. Malykhin (1999)

Commentationes Mathematicae Universitatis Carolinae

If a separable dense in itself metric space is not a union of countably many nowhere dense subsets, then its C p -space is not subsequential.

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

Anh Tran Mynard, Frédéric Mynard (2007)

Czechoslovak Mathematical Journal

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.

Dichotomies pour les espaces de suites réelles

Pierre Casevitz (2000)

Fundamenta Mathematicae

There is a general conjecture, the dichotomy (C) about Borel equivalence relations E: (i) E is Borel reducible to the equivalence relation E G X where X is a Polish space, and a Polish group acting continuously on X; or (ii) a canonical relation E 1 is Borel reducible to E. (C) is only proved for special cases as in [So].  In this paper we make a contribution to the study of (C): a stronger conjecture is true for hereditary subspaces of the Polish space ℝ ω of real sequences, i.e., subspaces such that [ y = ( y n ) n ∈ X ...

Examples of sequential topological groups under the continuum hypothesis

Alexander Shibakov (1996)

Fundamenta Mathematicae

Using CH we construct examples of sequential topological groups: 1. a pair of countable Fréchet topological groups whose product is sequential but is not Fréchet, 2. a countable Fréchet and α 1 topological group which contains no copy of the rationals.

Extension of multisequences and countably uniradial classes of topologies

Szymon Dolecki, Andrzej Starosolski, Stephen W. Watson (2003)

Commentationes Mathematicae Universitatis Carolinae

It is proved that every non trivial continuous map between the sets of extremal elements of monotone sequential cascades can be continuously extended to some subcascades. This implies a result of Franklin and Rajagopalan that an Arens space cannot be continuously non trivially mapped to an Arens space of higher rank. As an application, it is proved that if for a filter ℋ on ω , the class of ℋ -radial topologies contains each sequential topology, then it includes the class of subsequential topologies....

g -metrizable spaces and the images of semi-metric spaces

Ying Ge, Shou Lin (2007)

Czechoslovak Mathematical Journal

In this paper, we prove that a space X is a g -metrizable space if and only if X is a weak-open, π and σ -image of a semi-metric space, if and only if X is a strong sequence-covering, quotient, π and m s s c -image of a semi-metric space, where “semi-metric” can not be replaced by “metric”.

Hausdorff Fréchet closure spaces with maximum topological defect

Riccardo Ghiloni (2002)

Bollettino dell'Unione Matematica Italiana

It is well-known that the topological defect of every Fréchet closure space is less than or equal to the first uncountable ordinal number ω 1 . In the case of Hausdorff Fréchet closure spaces we obtain some general conditions sufficient so that the topological defect is exactly ω 1 . Some classical and recent results are deduced from our criterion.

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