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In this paper, we continue the study of function spaces equipped with topologies of (strong) uniform convergence on bornologies initiated by Beer and Levi cite{beer-levi:09}. In particular, we investigate some topological properties these function spaces defined by topological games. In addition, we also give further characterizations of metrizability and completeness properties of these function spaces.
For a non-isolated point $x$ of a topological space $X$ the network character $nw_chi(x)$ is the smallest cardinality of a family of infinite subsets of $X$ such that each neighborhood $O(x)$ of $x$ contains a set from the family. We prove that (1) e
A topological space $X$ is defined to have an $omega^omega$-base if at each point $xin X$ the space $X$ has a neighborhood base $(U_alpha[x])_{alphainomega^omega}$ such that $U_beta[x]subset U_alpha[x]$ for all $alphalebeta$ in $omega^omega$. We char
Our main problem is to find finite topological spaces to within homeomorphism, given (also to within homeomorphism) the quotient-spaces obtained by identifying one point of the space with each one of the other points. In a previous version of this pa
The structure of topological spaces is analysed here through the lenses of fibrous preorders. Each topological space has an associated fibrous preorder and those fibrous preorders which return a topological space are called spacial. A special class o
We prove that the semigroup operation of a topological semigroup $S$ extends to a continuous semigroup operation on its the Stone-v{C}ech compactification $beta S$ provided $S$ is a pseudocompact openly factorizable space, which means that each map $