SO

Sunday Oluyemi

Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, Oyo, Nigeria

2 Publications
0 Views
0 Downloads

Publications 2

1
Research Article Vol. 24, Issue 1

THE COUNTERPART OF A RESULT OF WEBB FOR THE BOUNDED DUAL Eb

SUNDAY OLUYEMI*

Denote by E, E+ andEb the continuous dual, the sequential dual and the bounded dual, respectively, of the lcs(E,τ). Well-known is that, [1, 22.2, p.87][2. Proposition 2.5.7, p.107], f ∈ E ⇐⇒ kerf is closed. John Webb added that, [5, Proposition 1.9., p.345], f ∈ E+ ⇐⇒ kerf is sequentially closed. I, hereby, add that f ∈ Eb ⇐⇒ kerf is locally closed...

Dec, 2015 Vol. 24, Issue 1
PDF
2
Research Article Vol. 24, Issue 1

FIVE SHORT NOTES ON BOUNDED MAPS

SUNDAY OLUYEMI*

This paper contributes five observations on bounded maps: (i) An observation on the definition of a bounded set, (ii) Three characterizations of bounded linear maps that parallel the usual general topology characterizations of continuity, (iii) An analogue of [2, PROPOSITION 3.12.1 p.254][7, Lemma 11.1.1, p.164] for bounded maps, (iv) That the Bana...

Dec, 2015 Vol. 24, Issue 1
PDF
Back to Articles