# Some theorems on equiconnected and locally equiconnected spaces

@article{Himmelberg1965SomeTO,
title={Some theorems on equiconnected and locally equiconnected spaces},
author={C. J. Himmelberg},
journal={Transactions of the American Mathematical Society},
year={1965},
volume={115},
pages={43-53}
}
• C. J. Himmelberg
• Published 1 March 1965
• Mathematics
• Transactions of the American Mathematical Society

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## References

SHOWING 1-10 OF 12 REFERENCES

### Retraction and extension of mappings of metric and nonmetric spaces

1. The two kinds of topological spaces that are called absolute retracts and absolute neighborhood retracts, were originally defined by BO~SUK ([5], [6]) for compact metric spaces. Later on these

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© Foundation Compositio Mathematica, 1956-1958, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les

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### On fibre spaces. II

This paper is primarily concerned with fibre mappings into an absolute neighborhood retract. Theorem 3 is a converse of the covering homotopy theorem; it characterizes fibre mappings (into a compact