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On the weak and pointwise topologies in function spaces
- Prelegent(ci)
- Mikolaj Krupski
- Afiliacja
- Uniwersytet Warszawski
- Termin
- 22 kwietnia 2015 16:15
- Pokój
- p. 5050
- Seminarium
- Seminarium „Topologia i teoria mnogości”
For a compact space K we denote by C_w(K) (C_p(K)) the space of
continuous real-valued functions on K endowed with the weak (pointwise)
topology. During the talk I would like to discuss the following basic
question which seems to be open:
Suppose that K is an infinite (metrizable) compact space. Is it true that C_w(K) and C_p(K) are homeomorphic?
I will show that the answer is "no", provided K is an infinite compact metrizable C-space. In particular the proof works for any infinite compact metrizable finite-dimensional space K.
Suppose that K is an infinite (metrizable) compact space. Is it true that C_w(K) and C_p(K) are homeomorphic?
I will show that the answer is "no", provided K is an infinite compact metrizable C-space. In particular the proof works for any infinite compact metrizable finite-dimensional space K.
