First countable and countable spaces all compactifications of which contain βN
Eric van Douwen, Teodor Przymusiński (1979)
Fundamenta Mathematicae
Similarity:
Displaying similar documents to “Tightness and resolvability”
First countable and countable spaces all compactifications of which contain βN
On weaker forms of compactness, Lindelöfness, and countable compactness.
Baboolal, D., Backhouse, J., Ori, R.G. (1990)
International Journal of Mathematics and Mathematical Sciences
Similarity:
A construction of a Fréchet-Urysohn space, and some convergence concepts
Aleksander V. Arhangel'skii (2010)
Commentationes Mathematicae Universitatis Carolinae
Similarity:
Some strong versions of the Fréchet-Urysohn property are introduced and studied. We also strengthen the concept of countable tightness and generalize the notions of first-countability and countable base. A construction of a topological space is described which results, in particular, in a Tychonoff countable Fréchet-Urysohn space which is not first-countable at any point. It is shown that this space can be represented as the image of a countable metrizable space under a continuous pseudoopen...
Countable fan-tightness versus countable tightness
Aleksander V. Arhangel'skii, Angelo Bella (1996)
Commentationes Mathematicae Universitatis Carolinae
Similarity:
Countable tightness is compared to the stronger notion of countable fan-tightness. In particular, we prove that countable tightness is equivalent to countable fan-tightness in countably compact regular spaces, and that countable fan-tightness is preserved by pseudo-open compact mappings. We also discuss the behaviour of countable tightness and of countable fan-tightness under the product operation.