Open set

In topology, an open set is an abstract concept generalizing the idea of an open interval in the real line. The simplest example is in metric spaces, where open sets can be defined as those sets which contain an open ball around each of their points (or, equivalently, a set is open if it doesn't contain any of its boundary points); however, an open set, in general, can be very abstract: any collection of sets can be called open, as long as the union of an arbitrary number of open sets is open, the intersection of a finite number of open sets is open, and the space itself is open. These conditions are very loose, and they allow enormous flexibility in the choice of open sets. In the two extremes, every set can be open (called the discrete topology), or no set can be open but the space itself (the indiscrete topology).

In practice, however, open sets are usually chosen to be similar to the open intervals of the real line. The notion of an open set provides a fundamental way to speak of nearness of points in a topological space, without explicitly having a concept of distance defined. Once a choice of open sets is made, the properties of continuity, connectedness, and compactness, which use notions of nearness, can be defined using these open sets.

Open (Blues Image album)

Open is Blues Image's second album and most acclaimed album, which featured the No. 4 hit single, "Ride Captain Ride".

Critical reception

Robert Christgau, writing in The Village Voice, wrote in a contemporary review: "Great single, mediocre (though improved) album. Do we really need another 'Parchman Farm?'"

Track listing

All songs by Blues Image except where noted.

Personnel

References

Open (Gotthard album)

Open is the fourth studio album released by the hard rock band Gotthard.

The album peaked at #1 on the Swiss Charts and was certified as 2x Platinum for exceeding 60,000 sales.

Track listing

All songs written by Steve Lee/Leo Leoni/Chris von Rohr except where noted.

Asian version (BMG AVCB-66072) adds the following

Personnel

Guests:

Open (sport)

An Open in sports terminology refers to a sporting event or game tournament that is open to contestants regardless of their professional or amateur status, age, ability, gender, sex, or other categorization. In many sports, preliminary qualifying events, open to all entrants, are held to successively reduce the field to a manageable number for participation in a final championship event, which itself may involve elimination rounds.

The term 'Open' may not be absolute. For example, in the U.S. Open in golf, entrants at qualifying events must have a USGA official handicap of 1.4 or less. Other minimum performance standards or eligibility criteria may apply in other sports.

Opens are usually found in golf, tennis, badminton, quizbowl, fighting games, snooker, darts, volleyball, ultimate, squash and chess.