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On semi-topological rings
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We introduce and study the semi-topological rings. Some examples of semi-topological rings are provided. We investigate some permanence properties of semi-topological rings. Along with other results, it is proved that translation of an open (resp. closed) set in a semi-topological ring is semi-open (resp. semi-closed), that multiplication of an open (resp. closed) set in a semi-topological ring by an invertible element of the ring is semi-open (resp. semi-closed). We also prove that any ring homomorphism between a semi-topological ring and a topological ring which is continuous at zero is semi-continuous everywhere.
MKD Publishing House
Title: On semi-topological rings
Description:
We introduce and study the semi-topological rings.
Some examples of semi-topological rings are provided.
We investigate some permanence properties of semi-topological rings.
Along with other results, it is proved that translation of an open (resp.
closed) set in a semi-topological ring is semi-open (resp.
semi-closed), that multiplication of an open (resp.
closed) set in a semi-topological ring by an invertible element of the ring is semi-open (resp.
semi-closed).
We also prove that any ring homomorphism between a semi-topological ring and a topological ring which is continuous at zero is semi-continuous everywhere.
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