On some generalizations of LC-spaces.
Dontchev, J., Ganster, M., Kanibir, A. (1999)
Acta Mathematica Universitatis Comenianae. New Series
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Dontchev, J., Ganster, M., Kanibir, A. (1999)
Acta Mathematica Universitatis Comenianae. New Series
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Aleksander V. Arhangel'skii (2010)
Commentationes Mathematicae Universitatis Carolinae
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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...
Hatzenbuhler, James, Mattson, Don A. (1979)
International Journal of Mathematics and Mathematical Sciences
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Peg Daniels (1995)
Commentationes Mathematicae Universitatis Carolinae
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We define -directedness, investigate various properties to determine whether they have this property or not, and use our results to obtain easier proofs of theorems due to Laurence and Alster concerning the existence of a Michael space, i.eȧ Lindelöf space whose product with the irrationals is not Lindelöf.
P. Moody, G. Reed, A. Roscoe, P. Collins (1991)
Fundamenta Mathematicae
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Angelo Bella, Viacheslav I. Malykhin (1998)
Commentationes Mathematicae Universitatis Carolinae
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We prove resolvability and maximal resolvability of topological spaces having countable tightness with some additional properties. For this purpose, we introduce some new versions of countable tightness. We also construct a couple of examples of irresolvable spaces.