Coreflectively modified continuous duality applied to classical product theorems.

*(English)*Zbl 1007.54008Author’s abstract: Several (old and new) results on stability of quotients (of various types) under product, on sequentiality of product of sequential spaces, on relationship between topology and the upper Kuratowski convergence on its closed sets are derived from a general mechanism of duality that uses the continuous convergence. Coreflectively modified biduals with respect to the continuous convergence lead to new reflectors which are of fundamental interest in this quest.

Reviewer: Miroslav Hušek (Praha 8)

##### MSC:

54B10 | Product spaces in general topology |

54D55 | Sequential spaces |

54B30 | Categorical methods in general topology |

06F30 | Ordered topological structures |

18B30 | Categories of topological spaces and continuous mappings (MSC2010) |

18D15 | Closed categories (closed monoidal and Cartesian closed categories, etc.) |

54B15 | Quotient spaces, decompositions in general topology |

54A20 | Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) |