### Citations

37 |
The Banach-Mazur Game and Banach Category Theorem
- Oxtoby
(Show Context)
Citation Context ... N) is won by α, or equivalently, if ⋂ n∈NBn ⊆ R for each t-play (Bn : n ∈ N). For more information on the BM(R)-game see [3]. Our interest in the BM(R)-game is revealed in the next lemma. Lemma 4.1 (=-=[9]-=-). Let R be a subset of a topological space X. Then R is residual in X if, and only if, the player α has a winning strategy in the BM(R)-game played on X. The next simple result plays a key role in th... |

11 | On hereditarily Baire spaces, σ-fragmentability of mappings and Namioka property, Topology Appl - Chaber, Pol - 2005 |

11 |
Infinite games and generalizations of first-countable spaces Gen
- Gruenhage
(Show Context)
Citation Context ...ced to: “Y is the product of hereditarily Baire metric spaces”. In this paper we substantiate this claim. The main result of this paper relies upon two notions. The first, which is that of a W -space =-=[6]-=-, is recalled in Section 2. The second, which is that of a “rich family” is considered in Section 3. In Section 4, we shall prove our main theorem which states that the product of a Baire space with a... |

10 | A survey on topological games and their applications in analysis’,
- Cao, Moors
- 2006
(Show Context)
Citation Context ... winning strategy if each play of the form ((Bn, tn(B1, B2, . . . , Bn)) : n ∈ N) is won by α, or equivalently, if ⋂ n∈NBn ⊆ R for each t-play (Bn : n ∈ N). For more information on the BM(R)-game see =-=[3]-=-. Our interest in the BM(R)-game is revealed in the next lemma. Lemma 4.1 ([9]). Let R be a subset of a topological space X. Then R is residual in X if, and only if, the player α has a winning strateg... |

9 | Jeux topologiques et espaces de - Raymond - 1983 |

8 | Oxtoby, Cartesian products of Baire spaces - C - 1961 |

7 | Separable determination of integrability and minimality of the Clarke subdifferential mapping - Borwein, Moors |

6 |
Barely Baire spaces, Fund
- Fleissner, Kunen
- 1978
(Show Context)
Citation Context ... X, ⋂n∈NOn is dense in X and a Baire space Y is called barely Baire if there exists a Baire space Z such that Y ×Z is not Baire. It is well known that there exist metrizable barely Baire spaces, (see =-=[5]-=-). On the other hand it has recently been shown that the product of a Baire space X with a hereditarily Baire metric space Y is Baire, [7]. In that same paper the author claims in a “Remark” that the ... |

4 |
The product of a Baire space with a hereditarily Baire metric space is Baire
- Moors
(Show Context)
Citation Context ...l known that there exist metrizable barely Baire spaces, (see [5]). On the other hand it has recently been shown that the product of a Baire space X with a hereditarily Baire metric space Y is Baire, =-=[7]-=-. In that same paper the author claims in a “Remark” that the hypothesis on Y can be reduced to: “Y is the product of hereditarily Baire metric spaces”. In this paper we substantiate this claim. The m... |

2 |
The product of totally nonmeagre spaces
- Aarts, Lutzer
- 1973
(Show Context)
Citation Context ... If a ∈ Πs∈SXs then Σs∈SXs(a) is a W -space. Corollary 2.6. [6, Theorem 4.1] If {Xn : n ∈ N} are W -spaces, then so is Πn∈NXn. Example 2.7. Suppose that S is a nonempty set. For each s ∈ S, let Xs := =-=[0, 1]-=- and define a : S → [0, 1] by, a(s) := 0 for all s ∈ S. Then by Theorem 2.5, X := Σs∈SXs(a) is a W -space. However, X is not first countable whenever S is uncountable. 3. Rich familes Let X be a topol... |