Nonseparating almost continuous retracts of 𝐼ⁿ

Author:

Rosen Harvey

Abstract

Compact almost continuous retracts of I n ( n 2 ) {I^n}(n \geqslant 2) do not separate E n {E^n} . Some other results that hold for continuous functions are also shown to hold for almost continuous functions. A result in [5] giving sufficient conditions for a set to be an almost continuous retract of I n {I^n} is examined further, and a method of constructing some almost continuous retracts of I n {I^n} is given.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference9 articles.

1. B. D. Garrett, Almost continuity, preprint.

2. Connectivity functions and retracts;Hildebrand, S. K.;Fund. Math.,1965

3. A connectivity map 𝑓:𝑆ⁿ→𝑆ⁿ⁻¹ does not commute with the antipodal map;Hunt, J. H. V.;Bol. Soc. Mat. Mexicana (2),1971

4. An almost continuous function 𝑓: 𝑆ⁿ→𝑆^{𝑚} which commutes with the antipodal map;Kellum, Kenneth R.;Proc. Amer. Math. Soc.,1976

5. On a question of Borsuk concerning non-continuous retracts. II;Kellum, Kenneth R.;Fund. Math.,1976

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