# equivalent of metric spaces and their topology [duplicate]

how we can give an example of two metrics on a space that induce the same topology , but are not equivalent!(so do we can generalize our definition about equivalent of metrics?)

## marked as duplicate by Lee Mosher general-topology StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Jun 19 at 15:34

Let $$(X,d)$$ be a metric space with $$d$$ unbounded and consider the metric $$d'(x,y)=\min\{d(x,y),1\}$$. This induces the same topology, but is not equivalent to $$d$$, since it is bounded

• short and sweet! – Prototank Jun 19 at 15:33