BAIRE SPACES AND QUASICONTINUOUS MAPPINGS

作者：Borsik Jan^*; Hola Lubica; Holy Dusan

来源：Filomat, 2011, 25(3): 69-83.

DOI：10.2298/FIL1103069B

• Quasicontinuous mapping
• equi-quasicontinuous sequence
• Baire space
• pointwise convergence
• topological convergence

The notion of quasicontinuity was perhaps the first time used by R. Baire in [2]. Let X, Y be topological spaces and Q(X,Y) be the space of quasicontinuous mappings from X to Y. If X is a Baire space and Y is metrizable, in Q(X,Y) we can approach each (x, y) in the graph Grf of f along some trajectory of the form {(x(k), f(nk)(x(k))) : k is an element of w} if and only if we can approach most points along a vertical trajectory. This result generalizes Theorem 5 from [3]. Moreover in the class of topological spaces with the property QP we give a characterization of Baire spaces by the above mentioned fact. We also study topological spaces with the property QP.

• 出版日期2011-9