Antipodal coincidence sets and stronger forms of connectedness
1985 ◽
Vol 31
(2)
◽
pp. 271-284
Keyword(s):
A new notion of α-connectedness (α-path connectedness) in general topological spaces is introduced and it is proved that for a real-valued function defined on a space with this property, the cardinality of the antipodal coincidence set is at least as large as the cardinal number α. In particular, in linear topological spaces, the antipodal coincidence set of a real-valued function has cardinality at least that of the continuum. This could be regarded as a treatment of some Borsuk-Ulam type results in the setting of general topology.