Sentence examples for preceding fact from inspiring English sources

Observe that the preceding fact shows a distinguishing feature of partial metric aggregation functions with respect to the metric ones.

The preceding fact is a special case of a general result for non-Archimedean spaces, that is, every continuous function from a connected space to a non-Archimedean space is constant.

Inspired by the preceding fact, we prove two fixed point theorems which provide the mathematical basis for a new technique to carry out asymptotic complexity analysis of algorithms via partial metrics.

The preceding facts yield the following result.

The preceding facts mentioned allow us to state the next useful result [3].

In connection with the preceding facts, we are now in a position to formulate a localization of Proposition 3 in the following form.

Taking into account the preceding facts we discuss the same properties in the case of projective Φ-contractions in the result below.

In connection with the preceding facts, we are now in a position to formulate a localization for lower edges contractions in the following form.

In connection with the preceding facts, based on Lemma 1 and Theorem 1, we are now in a position to formulate the following new statements as direct consequences of the Axiom of Infinite Choice.

Put the two preceding facts together and roughly one-third (31%) of all registered Delaware voters are Democrats in New Castle County, which is also the most educated, urban, wealthiest (highest median income), and racially diverse county in the state (Kent is a close second, and Sussex is a distant third).

These two preceding facts combined highlight the fact that HBV is very much present in our community.