Classification of Higher dimensional Erdos spaces by singular selectors

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It is well known that topologies generated by continuous weak selections are weaker than the original topologies. We call a space is CWS if the topology is generated by continuous weak selections. We have established the fundamental properties of CWS spaces and calculate the CWS numbers of several examples. Also we investigate the weak orderability of product spaces. As applications we show that if the product of a GO-space and a first countable space is weakly orderable, then the GO-space must be hereditarily paracompact. Also we have shown that a pseudocompact space without isolated point is homeomorphic to the Cantor set if and only ifits cube X×X×X is weakly orderable.