Small subsets of first countable spaces
Some counterexamples and properties on generalizations of Lindelöf spaces.
Some examples in the dimension theory of Tychonoff spaces
Some examples related to colorings
We complement the literature by proving that for a fixed-point free map the statements (1) admits a finite functionally closed cover with for all (i.e., a coloring) and (2) is fixed-point free are equivalent. When functionally closed is weakened to closed, we show that normality is sufficient to prove equivalence, and give an example to show it cannot be omitted. We also show that a theorem due to van Mill is sharp: for every we construct a strongly zero-dimensional Tychonov space...
Some m-dimensional compacta admitting a dense set of imbeddings into
Some Remarks On Choice Topology
Some remarks on choice topology.
Spaces with zero set bases
Stationary sets, trees and continuums.
Strongly irresolvable spaces.
Sum theorems for Ohio completeness
We present several sum theorems for Ohio completeness. We prove that Ohio completeness is preserved by taking σ-locally finite closed sums and also by taking point-finite open sums. We provide counterexamples to show that Ohio completeness is preserved neither by taking locally countable closed sums nor by taking countable open sums.