Weakly Fréchet–Urysohn and Pytkeev spaces

ε-weakly Chebyshev subspaces and quotient spaces

On the Pytkeev Property in Spaces of Continuous Functions (ii)

We prove that for each Polish space X , the space C(X) of continuous real-valued functions on X satisfies (a strong version of) the Pytkeev property, if endowed with the compactopen topology. We also consider the Pytkeev property in the case where C(X) is endowed with the topology of pointwise convergence.

On the Pytkeev Property in Spaces of Continuous Functions

Answering a question of Sakai, we show that the minimal cardinality of a set of reals X such that Cp(X) does not have the Pytkeev property is equal to the pseudo-intersection number p. Our approach leads to a natural characterization of the Pytkeev property of Cp(X) by means of a covering property of X, and to a similar result for the Reznichenko property of Cp(X).

ε-weakly chebyshev subspaces and quotient spaces

Weakly Continuously Urysohn Spaces

We study weakly continuously Urysohn spaces, which were introduced in [Z]. We show that every weakly continuously Urysohn w∆-space has a base of countable order, that separable weakly continuously Urysohn spaces are submetrizable, hence continuously Urysohn, that monontonically normal weakly continuously Urysohn spaces are hereditarily paracompact, and that no linear extension of any uncountabl...