Characterization of pseudocompactness by the topology of uniform convergence on function spaces
1978 ◽
Vol 26
(2)
◽
pp. 251-256
◽
Keyword(s):
AbstractIt is shown that a Tychonoff space X is pseudocompact if and only if for every metrizable space Y, all uniformities on Y induce the same topology on the space of continuous functions from X into Y. Also for certain pairs of spaces X and Y, a necessary and sufficient condition is established in order that all uniformities on Y induce the same topology on the space of continuous functions from X into Y.
1908 ◽
Vol 28
◽
pp. 249-258
1977 ◽
Vol 82
(2)
◽
pp. 297-300
◽
1979 ◽
Vol 31
(2)
◽
pp. 255-263
◽
1984 ◽
Vol 21
(03)
◽
pp. 654-660
◽
2005 ◽
Vol 178
◽
pp. 55-61
◽
1996 ◽
Vol 39
(3)
◽
pp. 275-283
◽