# A Banach-Dieudonné theorem for the space of bounded continuous functions on a separable metric space with the strict topology

@article{Kraaij2016ABT, title={A Banach-Dieudonn{\'e} theorem for the space of bounded continuous functions on a separable metric space with the strict topology}, author={Richard C. Kraaij}, journal={Topology and its Applications}, year={2016}, volume={209}, pages={181-188} }

## 2 Citations

### On equicontinuity and tightness of bi-continuous semigroups

- MathematicsJournal of Mathematical Analysis and Applications
- 2022

### Corrigendum to: ‘A Banach–Dieudonné theorem for the space of bounded continuous functions on a separable metric space with the strict topology’ [Topol. Appl. (2016) 181–188]

- MathematicsTopology and its Applications
- 2019

## References

SHOWING 1-10 OF 13 REFERENCES

### Bounded continuous functions on a completely regular space

- Mathematics
- 1972

Three locally convex topologies on C(X) are introduced and developed, and in particular shown to coincide with the strict topology on locally compact A1 and yield dual spaces consisting of tight,…

### Topological vector spaces

- Mathematics
- 2016

ing the above, for a (not necessarily countable) family . . . φ2 // B1 φ1 // Bo of Banach spaces with continuous linear transition maps as indicated, not recessarily requiring the continuous linear…

### On the Stone-Weierstrass theorem for the strict and superstrict topologies

- Mathematics
- 1976

Sentilles has introduced topologies 80, I8 and 81 on the space Cb(S) of all bounded, continuous, real-valued functions on the completely regular space S, which yield as dual spaces the three…

### Some forms of the closed graph theorem

- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 1971

In this paper we shall establish some forms of the closed graph theorem for locally convex spaces, using the approach of Pták(17). Our interest is in classifying pairs of locally convex spaces (E, F)…

### Sequential convergence in locally convex spaces

- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 1968

Abstract Given a locally convex Hausdorff linear topological space, we construct and examine the following topologies in the space: the finest locally convex topology with the same convergent…

### Topological Vector Spaces II

- Mathematics
- 1979

§ 14 contains the elementary theory of normed spaces and Banach spaces. A number of classical examples are discussed, to which we shall refer time and again in the later parts of the book.