In connection with a conjecture of Scheepers, Bukovský introduced properties wQN* and SSP* and asked whether wQN* implies SSP*. We prove it in this paper. We also give characterizations of properties S₁(Γ,Ω) and in terms of upper semicontinuous functions
A γ-space with a strictly positive measure is separable. An example of a non-separable γ−space with c.c.c. is given. A P−space with c.c.c. is countable and discrete.
Let X be a completely regular Hausdorff topological space and the space of continuous real-valued maps on X endowed with the pointwise topology. A simple and natural argument is presented to show how to construct on the space , if X contains a homeomorphic copy of the closed interval [0,1], real-valued maps which are everywhere discontinuous but continuous on all compact subsets of .
In the present paper we introduce a convergence condition and continue the study of “not distinguish” for various kinds of convergence of sequences of real functions on a topological space started in [2] and [3]. We compute cardinal invariants associated with introduced properties of spaces.
We show that if is first-countable, of countable extent, and a subspace of some ordinal, then is Lindelöf.