-spaces and images of separable metric spaces.
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Ge, Ying (2005)
Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]
P. Moody, G. Reed, A. Roscoe, P. Collins (1991)
Fundamenta Mathematicae
Bennet, Harold R., Martin, Harold W. (1977)
Portugaliae mathematica
Luong Quoc Tuyen (2013)
Matematički Vesnik
Vladimir Vladimirovich Tkachuk (1988)
Commentationes Mathematicae Universitatis Carolinae
Vladimir Vladimirovich Tkachuk (2018)
Commentationes Mathematicae Universitatis Carolinae
A space is functionally countable if is countable for any continuous function . We will call a space exponentially separable if for any countable family of closed subsets of , there exists a countable set such that whenever and . Every exponentially separable space is functionally countable; we will show that for some nice classes of spaces exponential separability coincides with functional countability. We will also establish that the class of exponentially separable spaces has...
Lowen-Colebunders, E. (1993)
Portugaliae mathematica
Maddalena Bonanzinga (1998)
Bollettino dell'Unione Matematica Italiana
W. W. Comfort, Ivan S. Gotchev (2016)
Gareth Fairey, Paul Gartside, Andrew Marsh (2005)
Commentationes Mathematicae Universitatis Carolinae
We examine when a space has a zero set universal parametrised by a metrisable space of minimal weight and show that this depends on the -weight of when is perfectly normal. We also show that if parametrises a zero set universal for then for all . We construct zero set universals that have nice properties (such as separability or ccc) in the case where the space has a -coarser topology. Examples are given including an space with zero set universal parametrised by an space (and...
Piotr Niemiec (2009)
Commentationes Mathematicae Universitatis Carolinae
A subset of a metric space is central iff for every Katětov map upper bounded by the diameter of and any finite subset of there is such that for each . Central subsets of the Urysohn universal space (see introduction) are studied. It is proved that a metric space is isometrically embeddable into as a central set iff has the collinearity property. The Katětov maps of the real line are characterized.
G. VIDOSSICH (1970)
Inventiones mathematicae
G. Reed (1972)
Fundamenta Mathematicae
R. Bennett (1972)
Fundamenta Mathematicae
Norbert Brunner (1982)
Monatshefte für Mathematik
J. Fernandez Novoa (1986)
Collectanea Mathematica
Vladimir Vladimirovich Tkachuk (2022)
Commentationes Mathematicae Universitatis Carolinae
We show that exponential separability is an inverse invariant of closed maps with countably compact exponentially separable fibers. This implies that it is preserved by products with a scattered compact factor and in the products of sequential countably compact spaces. We also provide an example of a -compact crowded space in which all countable subspaces are scattered. If is a Lindelöf space and every with is scattered, then is functionally countable; if every with is scattered, then...
McCoy, R.A. (1986)
International Journal of Mathematics and Mathematical Sciences
Eric van Douwen, Teodor Przymusiński (1979)
Fundamenta Mathematicae
Ronnie Levy, M. Matveev (2010)
Commentationes Mathematicae Universitatis Carolinae
A space is functionally countable (FC) if for every continuous , . The class of FC spaces includes ordinals, some trees, compact scattered spaces, Lindelöf P-spaces, -products in , and some L-spaces. We consider the following three versions of functional separability: is 1-FS if it has a dense FC subspace; is 2-FS if there is a dense subspace such that for every continuous , ; is 3-FS if for every continuous , there is a dense subspace such that . We give examples distinguishing...
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