On the generalized property
Marek Balcerzak (1986)
Mathematica Slovaca
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Marek Balcerzak (1986)
Mathematica Slovaca
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Andrzej Nowik, Patrick Reardon (2013)
Open Mathematics
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We prove that the Ellentuck, Hechler and dual Ellentuck topologies are perfect isomorphic to one another. This shows that the structure of perfect sets in all these spaces is the same. We prove this by finding homeomorphic embeddings of one space into a perfect subset of another. We prove also that the space corresponding to eventually different forcing cannot contain a perfect subset homeomorphic to any of the spaces above.
Balcerzak, M. (1993)
Acta Mathematica Universitatis Comenianae. New Series
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Jack Brown (1990)
Fundamenta Mathematicae
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M. N. Mukherjee, S. Raychaudhuri (1993)
Matematički Vesnik
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Isaiah Maximoff (1947)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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David Holgate (1998)
Commentationes Mathematicae Universitatis Carolinae
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We define perfect morphisms to be those which are the pullback of their image under a given endofunctor. The interplay of these morphisms with other generalisations of perfect maps is investigated. In particular, closure operator theory is used to link closure and orthogonality properties of such morphisms. A number of detailed examples are given.